# Calculus Questions

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Calculus

Limits & ContinuitySimplify for x in the third quadrant sin cos 1 X Enter the appropriate trig function Enter

Calculus

Limits & ContinuitySolve the equation and write the solution set x 5 16 0 If there is more than one solution list them in order from smallest to largest Do not enter any spaces in the answer The solution set is

Calculus

Limits & ContinuityGraph on the number line and express in interval notation The set of all real numbers between 2 and 4 including both 2 and 4 Choose the correct graph below O A O C 6 5 4 3 2 6 5 3 4 1 2 1 0 0 1 2 3 1 20 2 3 4 4 5 5 6 6 OB OD 6 4 5 4 6 5 4 3 3 2 1 0 1 2 1 0 1 Which of the following represents the set of all real numbers between 2 and 4 including both 2 and 4 expressed in interval notation OA 2 4 OD 2 4 OB B 2 4 OC 2 4 2 2

Calculus

Limits & ContinuityFind f x 1 when f x 4x x 5 To get full points show your work for this problem on your scratch paper

Calculus

Application of derivativesA function R x measures the revenue of a company in millions when producing x items Explain in your words the meaning of R 3200 1 25 For the toolbar press ALT F10 PC or ALT FN F10 Mac

Calculus

Application of derivativests to put a rectangular garden on her property using 64 meters of fencing There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the Fencing is then needed only on the other three sides Let x represent the length of the side parallel to the river Express the garden s area as a function of x full points show your work for this problem on your scratch paper

Calculus

DifferentiationFor the following quadratic complete the square to turn it into its vertex form f x 2x 12x 6

Calculus

Application of derivativesA line goes through the points 2 2 and 1 6 a Write the equation of the line in point slope form b Write the equation of the line in y intercept form Write the equation of the line in standard form n

Calculus

Vector Calculushe mathematical model p 0 01s2 0 8s 3 7 describes the percentage of college students p who are anticipating a starting salary s in thousands of dollars a Use the formula to find the percentge of students who anticipated a starting salary of 40 thousand h Does the starting slaary of 40 thousand have the highest percentage of students Explain

Calculus

Application of derivativesWhich of the following represents the X t signal in terms of unit ramp signals X t 3 1 a C e 1 2 3 3r t 5 r t 1 2r t 3 3r t 4 r t 2 r t 1 r t 2r t 2 3r t 3 r t 2 r t 1 2r t 3 3r t 4 r t 1 3r t 3 r t 2r t 2 3r t 5 2r t 4 r t 1 r t 3 3r t 4 r t 2 r t 2 3r t 4 r t 1 2r t 3 Br t 5 5 t

Calculus

Application of derivativesUse the graph below to state a the domain b range c where it is increasing d and decreasing using interval notation e x intercepts f local max g and mins Estimate values that are not clearly marked f x 5 3 2 1 5 4 3 2 1 0 1 2 3 4 12 B 45

Calculus

Application of derivativesConsider the equation f x x 2 5 Identify the parent function and describe ALL the transformations shifts stretches etc

Calculus

Vector CalculusFind the velocity and acceleration vectors in terms of u and up de T 2ea0 and 1 dt v u uo V

Calculus

Vector Calculusnd the velocity and acceleration vectors in terms of u and up a0 3e and do dt 2 GTX

Calculus

Vector CalculusIf f you already know lal and lvl then the formula a k v gives a convenient way to find the curvature Use it to find the curvature and radius of curvature of the curve r t cost t sin t i sin t t cos t j t 0 The curvature is

Calculus

Application of derivativesFind the length of the major axis of Earth s orbit using Kepler s third law and the fact that Earth s orbital period is 365 256 days Use G 6 6726 10 Nm kg M 1 99 x 1030 kg and 3 14 Recall that 1 N 1 kg m s 11 The length of the major axis of Earth s orbit is km Do not round until the final answer Then round to the nearest thousand as needed

Calculus

Application of derivativesb Evaluate the differential df x y f P dx f P dy for dx 0 5 dy 0 3 and P 1 1 10p

Calculus

Application of derivatives4 a Find average value of f x y 10xy over the region R given in the Figure Average value of f over R b Let I ill 1 area of R f dA x y dx dy y 2 x 15p

Calculus

Limits & Continuitya the limit lim y 4 x y 2 4 x y xy 4x 4x af b Use chain rule to evaluate du if x y x xy y and x u sin v at u 1 v y u cos v 10p 1

Calculus

Definite IntegralsFind the volume of the region D bounded above by the spher x y z 360 and below by the paraboloid 2z x y

Calculus

Definite Integrals1 a Use the formula to find the length of the indicated portion of the curve r t t sint cost i t cost sint j 4k 0 t n L B dt 2 dz dt 2 dt 15p

Calculus

Differential equationsIF a parabolic mirror passes through the points 0 0 and 10 4 find the focal point

Calculus

Differential equations1 point Find a function f x so that h x g f x given that g x 5x 2x 2x 3 and h x 5 2x 2 2 2x 2 2 2x 2 x

Calculus

Vector CalculusShow all work No Calculator is allowed 1 Graph one cycle of the graph of f Label the intercepts and the high low points F x 5cosx 6x n 2

Calculus

Indefinite Integrationtan x 7 tan x 12 Step 2 Rewrite the polynomial in the denominator as u 7u 12 u 4u 1 u 7u 12 where A and B are to be determined U 3 Collect the terms according to the power of u on the right side and factorize u 7u 12 u u 4 3 u 4 u 4 u 3 Because u 7u 12 u 4 u 3 you should include one partial fraction for each factor and write B A U 4 1 U 4 Rey 3 u 12 U Step 3 Multiplying this equation by the least common denominator u u 3 yields the basic equation 3 B u 4 7 7 u 12

Calculus

Indefinite Integrationet 24 ex 20 dx 5 88 Points DETAILS LARCALCET7 8 5 031 MI Use substitution and partial fractions to find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration x

Calculus

Differential equations0 5 88 Points DETAILS PREVIOUS ANSWERS dx LARCALCET7 8 5 015 Use partial fractions to find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration 7 x

Calculus

Indefinite Integrationx 4x 1 5 88 Points DETAILS LARCALCET7 8 5 009 Use partial fractions to find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration 2x 16x 39x 32 dr

Calculus

Indefinite Integration5 x x 1 True False A can be put in the form X B 2 X 1 I where A and B are constants

Calculus

Application of derivativesFind the quotient and remainder using long division 6 x6 3x4 4x x2 3 quotient remainder 12

Calculus

Limits & ContinuityvFind the equation of the line in slope intercept form tangent to fat x 1

Calculus

Vector Calculus36 You have a wire that is 71 cm long You wish to cut it into two pieces One piece will be bent into the shape of a right triangle with legs of equal length The other piece will be bent into the shape of a circle Let A represent the total area enclosed by the triangle and the circle What is the circumference of the circle when A is a minimum

Calculus

Vector CalculusIf Ps is a monic quintic polynomial for which Ps 2 cost 2 cos 5t for all angles t then A Ps x x 5x 5x B Ps x 3x 5x C P x x 5x I D Ps x x 6x 4x E Ps x x 7x 3x

Calculus

DifferentiationConsider the equation f x x 4 7 Identify the parent function and describe ALL the transformations shifts stretches etc 3

Calculus

Application of derivativesThinking about transformations most basic functions can be thought of in the following forms where the lower case letters a through d have the same meaning y a bx c d y asin bx c d y ae bx c d Match each of the lowercase letters with their role v b VC vd 1 left right shift II horizontal compression stretch III vertical compression stretch IV up down shift

Calculus

Limits & ContinuityMatch the description with each form of a line Slope Intercept Point Slope Standard Form Horizontal Line A Ax By C 0 B y y m x x C y b D y mx b

Calculus

Vector Calculusa Sketch the region bounded by y x y x 10 b Find the area of the bounded region J x dx f vdx 32 2 4 4 un units X X x X x x 0 x x 1 0 X 0 1 7 6

Calculus

Limits & Continuitynd the equation of the tangent line to the graph of f x at the given point f x 27x 54 at 1 9

Calculus

Application of derivatives5 We have accidentally introduced a new bacteria in our pond and their growth rate can be described using an exponential model a Given that their population is 5 times the initial population after 2 days what is the exponential growth constant k b How many days will it take to reach 20 times the initial population

Calculus

Definite Integrals4 For the following problem a Sketch the region bounded by y x y x b Find the area of the bounded region

Calculus

Definite Integralsoint Suppose luate the definite integral by interpreting it in terms of signed area 0 f x dx f x 3x 15 15 3c if 0 5 if 5 10 gestion Draw a picture of the region whose signed area is represented by the integral Then find the signed area using formulas from high school geometr

Calculus

Application of derivativesThe square region with vertices 13 0 26 13 13 26 and 0 13 is revolved about the x axis to generate a solid Find the volume and surface area of the solid

Calculus

Application of derivativesHow many license plates can be made using either three uppercase English letters followed by three digits or four uppercase English lettem followed by two digits

Calculus

Application of derivativesUse the given graph of the derivative f of a continuous function f over the interval 0 9 to find the following ya 2 0 2 y f x 2 4 6 18 x a On what interval s is fincreasing Enter your answer using interval notation 1 x 6 x 8 On what interval s is f decreasing Enter your answer using interval notation 0 x 1 6 x 8 b At what value s of x does f have a local maximum Enter your answers as a comma separated list x 6 At what value s of x does f have a local minimum Enter your answers as a comma separated list x 1 8 c On what interval s is f concave upward Enter your answer using interval notation 0 x 6 6 x 9 On what interval s is f concave downward Enter your answer using interval notation 2 3 U 5 7 d What are the x coordinate s of the inflection point s of Enter