Calculus Questions

Use technology to find points and then graph the function y 2log 2 8 1 following the instructions below done plotting points Plot at least five points with integer coordinates that fit on the axes below Click a point to delete it

4 1 Determine the absolute maximum and minimum values for the function below on the given interval K f x x 3x 6 x 6x where 0 x 4 2 Minimum Value at x

9 The difference between two numbers is k Show that their product is at least 0 25k Interval not needed

2 Determine the absolute extrema of the function on the closed interval given K f x 4x x 1 where x 0 4

8 A boat leaves a dock at 2 00 pm heading west at 15 km h Another boat heads south at 12 km h and reaches the same dock at 3 00 pm At what time were the boats closest to each other Round to 2 decimal places Interval not needed

4 1 Determine the absolute maximum and minimum values for the function below on the given interval K 1 5 S x x x 6x where 0 x 4 3 2 Minimum Value at x

9 The difference between two numbers is k Show that their product is at least 0 25k Interval not needed

4 A car rental agency has 200 cars The owner finds that at a price of 36 per day he can rent all the cars For each 2 increase in price the demand is less and 5 fewer cars are rented What price will maximize the total revenue A Interval

Determine the absolute extrema of the function on the closed interval given K f x 4x x 1 where x 0 4

2 7 Finding where the derivative of a function equals zero will always produce the desired optimal value Is this statement true or false Explain your reasoning C

6 Explain why we cannot determine maximum or minimum values for the function f x X x 3 interval 5 x 5 Include in a sketch in your solution C over the

5 A cylindrical tank with no top is to be built from stainless steel with a copper bottom The tank is to have a volume of 5 m If the price of copper is five times the price of stainless steel what should be the dimensions of the tank so that the cost is a minimum Interval not needed A Vcylinder h SACylinder 2tr 2 rh

6 of the swimming area is a straight sandy beach and the rope will form the other three sides Determine the dimensions of the rectangle that produces the maximum swimming area Determine the dimensions that would produce the largest swimming area A Interval

nalyze the polynomial function f x x x 5 using parts a through h below Determine the end behavior of the graph of the function he graph of f behaves like y for large values of x

3 ex f x nv uv 3 e x ex 3 6 ubtex xe u s ex livtur e e x e xe V 3 ex v 9 62 12 va 6e 2e 31 J 2 Cafilah derivative f x 6x x ex 3x

65 A family of curves has polar equations 1 a cos 0 1 a cos 0 Investigate how the graph changes as the number a changes In particular you should identify the transitional values of a for which the basic shape of the curve changes

Hiring nilai us X 2x J 1 x

Use l Hopital s Rule to evaluate the limit cos 3x 1 x2 17 lim x 0 A 18 lim x sin X 8 A 1 5x B 0 B 0 C 3 20 C 1 2 2 D D 5 17 18

Use l Hopital s Rule to evaluate the limit cos 3x 1 17 lim X 8 x2 A 96 B 0 6 3 2 D

Find all zeros of the polynomial Enter your answers as a comma separated list Enter all answers including repetitions P x 2x 9x 16x 15 X 5 2 27 1 2i 1 X Your answer cannot be understood or graded More Information

4 Points DETAILS SPRECALC7COREQ 3 5 001 The polynomial P x 5x x 2 x 8 has degree It has zeros 0 2 and The zero 0 has multiplicity and the zero 2 has multiplicity

Factor the polynomial completely Q x x 256 Q x Find all its zeros State the multiplicity of each zero Order your answers from smallest to largest real followed by complex answers ordered smallest to largest real part then smallest to largest imaginary par with multiplicity X X X X with multiplicity with multiplicity with multiplicity

Factor the polynomial completely P x x5 2x3 P x Find all its zeros State the multiplicity of each zero Order your answers from smallest to largest real followed by complex answers ordered smallest to largest real part then smallest to largest imaginary with multiplicity X X X with multiplicity with multiplicity

1 Points Find all zeros of the polynomial Enter your answers as a comma separated list Enter all answers P x x 5x 35x 5x 36 X

So far we have worked only with polynomials that have real coefficients This exercise involves polynomials with real and imaginary coefficients Find all solutions of the equations Enter your answers as comma separated lists Enter all answers including repetitions a 2x 18i 1 X b X c X d X x 4ix 0 x 6ix9 0 ix 2x i 0

A polynomial P is given P x x 15x 16 a Factor P into linear and irreducible quadratic factors with real coefficients P x b Factor P completely into linear factors with complex coefficients P x

Find a polynomial with integer coefficients that satisfies the given conditions Q has degree 3 and zeros 3 2i and 21 Q x

Given the graph of f x below find the graph of the derivative of f x Select the correct answer below 6 5 4 3 2 SH Y N 3 4 5 6

51 54 Find the points on the given curve where the tangent line is horizontal or vertical 51 r 3 cos 0 53 r 1 cos 0 52 r e 54 r sin 20

Find the open interval s of f x graph given below where f x is negative 6 Provide your answer below S 43 4 3 2 6 5 4 3 2 1 1 2 3 4 5 6 5 6 Give your answer in interval notation For example 2 4 U 6 00 141

5 and p Construct a Binomial probability distrubtion table using n 0 24 Next record the mean am standard deviation of the distribution below Where necessary round all numbers to four decimal places x P x

57 60 Use a graphing device to graph the polar curve Choose the parameter interval to make sure that you produce the entire curve STUT 0 57 r esin 2 cos 40 butterfly curve

The graph of function f x is shown below At which value of x is the derivative of the function equal Select the correct answer below Ox 4 0 3 O x 2 Ox 1 0x 0 HIN 6 5 4 3 2 1 3 2 1 3 1 2

47 50 Find the slope of the tangent line to the given polar curve at the point specified by the value of 0 47 r 2 sin 0 0 6 48 r 2 sin 0 0 3

2 Consider the series n 1 n 2 n 1 a x Use your computer to graph the functions f x 32 and g x 3 2 on the same set of axes You can use Desmos or your graphing calculator Set the scale on the horizontal axis so the x values go from 1 to 100 We are interested in comparing the functions for large values of x and when x is large both f x and g x are quite small Thus you should set the scale on the vertical axis to view the y values between 0 and 1 If you are using Desmos use the wrench button at the top right of your screen to set the vertical scale b Now use your computer to plot the function f x from part a together with h x You may have to experiment to find a range of y values that will enable you to see both functions on the same axes f x f x limx and limx h for the functions in parts a and b c Calculate above You can do this by hand or use the graphs of the quotients on desmos and see what happens as x goes to You don t have to show your work here but what are the limits d Look at the results of parts a through c and the statement of the LCT Should 1 you compare the series En 1 n 2 7 with n 1 7 2 or with n 1 Explain your choice after considering which term dominates the denominator for large values of n n 1n n e Does the series n 1 n 2 n converge Use the LCT and your knowledge of p series to justify your conclusion

Given the graph of f x below what is the open interval s over which f x is positive 6 5 4 3 H 1 2 3 4 5 6

Divide 1 m 7m 11 m 8 61

Given the graph of f x below identify the graph of f x 6 5 4 3 2 1 6 5 4 3 1 2 3 4 31 H 1 2 3 4 5 6

In the process of finding the inverse of the following matrix explain the indicated row operation 3 3 6 1 0 0 1 3 10 0 10 1 3 5 0 0 1 Step 1 Switch row 1 and row 2 1 3 1 3 Answer to Step 1 Step 2 Explain the row operation to change the answer from Step 1 to the result below 1 3 10 0 1 0 6 24 1 3 0 3 5 0 Answer to Step 2 0 3 10 0 1 3 6 100 5 0 0 1 1 0 1

HIV JR Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once c Determine the real zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x intercept The real zero s of f is are 0 7 Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once n below The lesser zero of the function is of multiplicity 2 so the graph off touches the x axis at x 0 The greater zero of the function is of multiplicity 1 so the graph of f crosses the x axis at x 7 d Use a graphing utility to graph the function The graphs are shown in the viewing window Xmin 20 Xmax 20 Xscl 2 Y min 100 Ymax 100 Yscl 10 Choose the correct graph below OA B Q O C D 10

Find the dimensions of a rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 100 feet of fencing help numbers Width Length help numbers

question You can retry this question below A large company determines that in t months the number of units in the thousands that they will have 11t 3 produced is given by p t t 4 dollars Question Help Message instructor What will happen to the production in the long run

The graph of y f x is shown Assume f x is continuous 8 7 6 5 4 3 2 Find xf x 12 lim x4 f x x 13 Question Help Mu 1 8 7 6 5 4 3 2 1 2 3 4 5 6 7 1 8 1 2 3 4 5 6 7 q

Suppose f x and g x have the following values f 8 4 and f 8 6 g 8 1 and g 8 1 Assume all functions are continuous Find the following f x 3f x 4 lim

Evaluate the limit lim 3 tan 4x Enter a simplified multiple of or or x48

Suppose f 2 8 f 2 9 g 2 3 g 2 1 and that f x g x are continuous for all x f x 8 lim x2 g x 3 Question Help O Cannot Be Determined Video Message instructor

Question 12 Evaluate lim sin 9x o A

Evaluate the limit using L H pital s rule 7x lim X18 e5x

Quest no Evaluate the limit using L H pital s rule X e 2x 1 6x lim x 0

Question 4 lim x 0 Evaluate the limit using L Hospital s rule 4 5 X