Calculus Questions

a Find the area of the triangle determined by the points P Q and R b Find a unit vector perpendicular to plane PQR P 1 1 0 Q 0 0 1 R 0 0 1 a The area of the triangle is Type an exact answer using radicals as needed

Sketch the coordinate axes and then include the vectors u v and u xv as vectors starting from the origin u 9i v 8j Which of the following graphs contains u v and u xv O A O C X uxv z u z uxy O B O D uxv X x Z u z y y uxv

Given nonzero vectors u v and w use dot product and cross product notation as appropriate to describe the following a The vector projection of u onto v b A vector orthogonal to u and v c A vector orthogonal to u xv and w d The volume of the parallelepiped determined by u v and w e A vector orthogonal to u xv and uxw f A vector of length u in the direction of v a Which of the following describes the vector projection of u onto v O A OB O C U V u u V u V V V V

Graph the logarithmic function f x log x 1 Drag the two blue points on correct line graph to the correct points that f x passes through Then use the remaining red point to drag the vertical asymptote to the Note that the points drag in increments of fourths Y

Graph the logarithmic function f x log x 4 Drag the two blue points on graph to the correct points that f x passes through Then use the remaining red point to drag the vertical asymptote to the correct line Note that the points drag in increments of fourths

Condense the left hand side into a single logarithm log 9 log x log y log IED help formulas

Use the properties of logarithms to expand the following logarithm as much as possible Rewrite as a sum difference or product of logs log r y r y7

Expand log 34 to rewrite as a sum difference or product of logarithms Choose all correct answers There may be more than one way to rewrite the expression A log a log b c4 OB log a log b log c OC 2 log a 3 log b 4 log c OD 2 log a 3 log b 4 log c OE log a log b c4 OF None of the above

Use the properties of logarithms to expand the following logarithm as much as possible Rewrite as a sum difference or product of logs log

Expand In expression A In 4 In k OB kln 4 OC In 1 k ln 4 OD In 1 In 4 OE In 1 In 4 to rewrite as a sum difference or product of logarithms Choose all correct answers There may be more than one way to rewrite the OF None of the above

Condense the left hand side into a single logarithm log a log b log c log 4 help formula

Expand In 14xy to rewrite as a sum difference or product of logarithms Choose all correct answers There may be more than one way to rewrite the expression A In 14 In z ln y B 14 ln zy In 14 In ry DC OD 14 ln z 14 ln y E In 2 In z ln y ln 7 F None of the above

Use properties of logarithms to evaluate without using a calculator 2 log 4 log4 256 3 log 6561

Use graphing technology to find approximate solutions of log 6x 3 4 4 log 6x 3 help numbers X

7 pts Using Theorem 8 Maximum Minimum Principle 1 find the absolute maximum and absolute minimum values of the function if they exist over the indicated interval nobisnut gevie f x x 3x2 9x 7 on 2 2 allmos

The shape of a colony of bacteria on a Petri dish is circular Find the approximate increase in its area if its radius increases from 10 mm to 19 mm Recall that the area of a circle is A

A cube with sides 9 inches long is covered with a coat of fiberglass 0 6 inch thick Use differentials to estimate volume of the fiberglass shell THE The volume of the fiberglass shell is approximately in

pv 11 nv 0 234 a Identify the individual variable random variable X and the random variable in the context of this problem The individual is a randomly selected college student The variable information collected from each individual is the percentage of 234 randomly selected college students that are left handed X The wording in context for the random variable X is as follows rv X the number of 234 randomly selected college students that are left handed The wording in context for the random variable is as follows rv p the percentage of 234 randomly selected college students that are left handed b Can we say that the sampling distribution of p is approximately normal A Yes Because np 25 74 o which is v n 1 P 208 25 x which is v B008 0 11 10 O 10 OB 8 c What is the probability that no more than 9 of the randomly selected college students are left handed Round final answer to 4 decimal places

Filing status single Gross income 75 000 Adjustments 7000 Deductions 11 500 mortgage interest 4100 property taxes 2000 charitable contributions Tax credit none Click the icon to view the 2021 marginal tax rates he income tax owed is SLITE

Consider the following function If an answer does not exist enter DNE 7 x a Find the vertical asymptote s Enter your answers as a comma separated list x 0 f x 1 5 X Find the horizontal asymptote s Enter your answers as a comma separated list y 1 b Find the interval s of increase Enter your answer using interval notation Find the interval s of decrease Enter your answer using interval notation c Find the local maximum and minimum values local maximum value local minimum value d Find the interval s on which f is concave up Enter your answer using interval notation Find the interval s on which f is concave down Enter your answer using interval notation Find the inflection point x y e Use the information from parts a d to sketch the graph of f y y

Find an equation of the slant asymptote Do not sketch the curve 3x4 x x x x 3 y y X Enhanced Feedback Please try again keeping in mind that if lim X 8 f x mx b 0 or lim X 18 f x mx b 0 then th

Let p 21 x and C x 746 2x where x is the number of garden hoses that can be sold at a price of p per unit and C x is the total cost in dollars of producing x garden hoses A Express the revenue function in terms of x B Graph the cost function and the revenue function in the same viewing window for 0 x 441 Use approximation techniques to find the break even points

The price p in dollars and the demand x for a particular clock radio are related by the equation x 5000 50p A Express the price p in terms of the demand x and find the domain of this function B Find the revenue R x from the sale of x clock radios What is the domain of R C Find the marginal revenue at a production level of 2800 clock radios D Interpret R 4400 76 00

dy dx the given points e equation 0 r 30 0 0 At 0 f 0 sin 0 f 0 cos f 0 cos 0 f 0 sin 0 A T 0 0 the slope of the curve is 1 ype an exact answer 2 10 0 the value of the second derivative is and so the curve is Type an exact answer A te the slope of the curve is 1 2 Type an exact answer gives a formula for the derivative y of a polar curve r f 0 The second derivative is the value of the second derivative is 1 and so the curve is 2 d y dy de 2 dx de dx Find the slope and concavity of the following curv

The total cost in dollars of manufacturing x auto body frames is C x 40 000 200x A Find the average cost per unit if 50 frames are produced B Find the marginal average cost at a production level of 50 units C Use the results from parts A and B to estimate the average cost per frame if 51 frames are produce

Use power series operations to find the Taylor series at x 0 for the following function 13xe The Taylor series for ex is a commonly known series What is the Taylor series at x 0 for e 80 Type an exact answer n 0 Use power series operations and the Taylor series at x 0 for ex to find the Taylor series at x 0 for the given functio 8 Type an exact answer 1 n 0

Find the indicated quantities for y f x 2x f 4 Ax f 4 A Simplify Ax B What does the quantity in part A approach as Ax approaches 0 A f 4 Ax f 4 Ax 11

Find the following for the vectors v 10i 2k and u i j k a v u v u b the cosine of the angle between v and u c the scalar component of u in the direction of v d the vector proj u a v u 8 Type an exact answer using radicals as needed v 2 26 Type an exact answer using radicals as needed u 3 Type an exact answer using radicals as needed 4 b The cosine of the angle between v and u is 78 Type an exact answer using radicals as needed 4 26 c The scalar component of u in the direction of v is Type an exact answer using radicals as needed d proj u Type your answer in terms of i j and k Type an exact answer using radicals as

Find the following for the vectors v 2i 3j 6k and u 7i 24j a v u v lul b the cosine of the angle between v and u c the scalar component of u in the direction of v d the vector proj u a v u 86 Type an exact answer using radicals as needed v 7 Type an exact answer using radicals as needed u 25 Type an exact answer using radicals as needed 86 b The cosine of the angle between v and u is 175 Type an exact answer using radicals as needed 86 7 c The scalar component of u in the direction of v is Type an exact answer using radicals as needed d proj u Type your answer in terms of i j and k Type an exact answer using radicals as neec

Find the following for the vectors v 10i 2k and u i j k a v u v u b the cosine of the angle between v and u c the scalar component of u in the direction of v d the vector proj u a v u 8 Type an exact answer using radicals as needed v 2 26 Type an exact answer using radicals as needed u 3 Type an exact answer using radicals as needed 4 78 Type an exact answer using radicals as needed c The scalar component of u in the direction of v is Type an exact answer using radicals as needed b The cosine of the angle between v and u is

Find the length of the following curve 2t 7 3 2 3 X y 3t 0sts2 The length of the curve is Simplify your answer

9 sin 0 4 cos 0 Replace the polar equation r The equivalent Cartestian equation is y 0 Choose the correct graph below OA with an equivalent Cartesian equation Then identify the graph B O C 10 O D

Find the polar coordinates 0 0 2n and r20 of the following points given in Cartesian coordinates a 1 3 b 2 2 2 2 c 2 3 2 a The polar coordinates of the point 1 3 are Q Type an ordered pair Type an exact answer using as needed Type any angles in radians between 0 and 2 b The polar coordinates of the point 2 2 2 2 are 0 Type an ordered pair Type an exact answer using as needed Type any angles in radians between 0 and 2 c The polar coordinates of the point 2 3 2 are 0 Type an ordered pair Type an exact answer using as needed Type any angles in radians between 0 and 2

Find the Taylor polynomials of orders 0 1 2 and 3 generated by fat a f x x a 0 P x Simplify your answer P X P X 0 Py x

Find parametric equations and a parameter interval for the motion of a particle starting at the point 3 0 and tracing the top half of the circle x y 9 two times Choose a correct possible parametrization below O A x 3 cost y 3 sint Ost 2 OB X 3 cost y 3 sint Ost 2 O c x 3 cost y 3 sint 0 t T OD x cost 3 y sin t 3 1 Ost 2

Given a function p x x x 2 x 2 A Explain why the Mean Value Theorem applies to p x on the interval 1 2 Find the point s guaranteed to exist by the Mean Value Theorem

The amount of money SB in a bank account earning interest at a continuous rate r depends on the amount deposited P and the OB OB t r and time t it has been in the bank where B Pert Find OB OP OB t OB represents the change in the t amount of money in the bank JB r OB r OB OP and interpret each in financial terms OB OP Pret Ptert represents the change in the amount of money in the bank X represents the change in the as one unit of time passes by as the interest rate changes Choose one

Rewrite the function using the power reducing formulas f x 4 sin x f x X Use a graphing utility to graph the function y 1 5 1 0 0 5 2 1 5 1 0 0 5 0 5 1 0 1 5 y 2 d 0 5 2 1 0 1 5 X 1 5 1 0 1 5 0 5 1 0 0 5 y 2 y 2 0 5 0 5 1 0 1 0 1 5 1 5 X M J

Find the area enclosed by the given curves 12 y x y 4x A 8 B 16 C 2

Find the derivative S A 5x 6 14 dt 5t 6 B 5x 6 1 5 5x 6 2 C D 5 XE

3 2 3 O O 6 7 8 q The graph above shows the velocity of an object as a function of time Time is measured in seconds velocity in meters per second If the object s initial location is 0 meters where is it at t 8s h 8 m If the object s initial location is 2 meters where is it at t 8s h 8 m

Speedometer readings for a vehicle in motion at 3 second intervals are given in the table t sec 6 9 12 15 18 0 3 0 9 v ft s 31 56 71 68 50 Estimate the distance traveled by the vehicle during this 18 second period using a left sum L6 a right sum R6 and a middle sum M3 L6 705 R6 855 M3 474 Question Help Add Work feet feet x feet Video

Given the function graphed below evaluate the definite integrals 4 3 2 1 1 2 3 7 2 4 2 s f x dx f x dx Question Help Video Add Work 6 q

Question 10 The graph of g is given below 6 5 4 3 2 1 6 5 4 3 g x dx 1 1 2 3 4 5 6 N 1 3 4 5 6 Use the graph to evaluate each definite integral 2 9 2 9 a dx 9 x dx 9 x dx 9 2 dx 9 x dx a da 19 x 8 dx

Suppose we want to approximate the integral b x dx by using a left hand sum with 4 rectangles of equal widths Write out this sum using function notation for each term Answer Now approximate the integral b a da by using a right hand sum with 3 rectangles of equal widths Write out this sum using function notation for each term Answer

Next question Evaluate the integral below by interpreting it in terms of areas in the figure The areas of the labeled regions are A1 7 A2 3 A3 1 and A4 1 V f f x da V 55 5 X Get a similar question Question Help Video Add Work You can retry this question below 0 A1 y f x 3 A2 LO 5 A3 7 A4 figure is NOT to scale 10

Estimate the areas under the curve by computing the left Riemann sum Lg 11 1 8 8

Evaluate the integral 16 22 dx by interpreting it in terms of area In other words draw a picture of the region the integral represents and find the area using geometry 16x dx 16 Holn Written Example

The following limit of right Riemann sums can be expressed as a definite integral n 7 7i 2 5 3 7 7 2 1 n n i 1 lim n In the integral b f x f a da

2 Next question The graph below shows a rectangular sum of n 4 rectangles to approximate the area under the line from x 0 to 2 4 14 13 12 11 10 9 8 7 6 5 4 3 2 Get a similar question You can retry this question below Is this a right hand or left hand sum left hand sum y What is the equation of the line What is the value of the sum 3 6 Complete the notation for the sum of the areas of all 4 rectangles