Calculus Questions

identify a1 r and n for the sum of the geometric series 1 2 38 9 32 27 128 81 512

Find the derivative of the following function y 3 11X

Find the derivative of the following function A 630 1 708 A

Consider the following curve 2 cos 20 25 Write an equation for the curve in terms of sin 8 and cos 8 Find a Cartesian equation for the curve Identify the curve ellipse circle Ohyperbola Oline Olima on Need Help Read

We are given the point in polar coordinates 9 7 We are asked to find two other pairs of polar coordinates to represent the point one with the radius r 0 and one with r 0 We can plot the point which creates an angle of counterclockwise with the polar axis in other words the positive horizontal axis The radius or distance from the origin is r 9 4 O 4 93 To find a second pair of polar coordinates for the same point that has radius r 0 we must use the same value r 9 This is the unique positive number to represent the distance of 9 from the point to the origin The angle as not unique however as adding any multiple of 2 results in the same angle Therefore we can add 2 to the angle of the given polar coordinates to find a second point as follows

Find a Cartesian equation for the curve r 3 cos 0 Identify the curve circle Olima on Oline O ellipse Ohyperbola

The demand for a new computer game can be modeled by p x 43 5 3 In x for 0 x 800 where p x is the price consumers will pay in dollars and x is the number of games sold in thousands Recall that total revenue is given by R x x p x Complete parts through c below a Find R x R x b Find the marginal revenue R x R x c How many units will be sold if the price that consumers are willing to pay is 40 The number of units that will be sold is Round to the nearest whole number as needed

Vrea sin gr dr ria Vore sin gr dr Va rla a q 1 aq a q r 2a r cos gr a q a q r a r sin qr 2V a q a q 1

Students in a zoology class took a final exam They took equivalent forms of the exam at monthly intervals thereafter After t months the average score S t as a percentage was found to be given by the following equation where t20 Complete parts a through e below S t 81 15 In t 1 Osts80 a What was the average score when they initially took the test The average score was Round to one decimal place as needed b What was the average score after 4 months The average score after 4 months was Round to one decimal place as needed c What was the average score after 24 months The average score after 24 months was Round to one decimal place as needed d Find S t S t e Find S 4 and S 24 and interpret the meaning of these numbers S 4 which means that after 4 months the average score is Type integers or decimals by points a month and S 24 which means that after 24 months the average score is by points a month

Find a Cartesian equation for the curve 2 13 Identify the curve Oline O hyperbola O ellipse O lima on O circle

a 5 5 We are given the Cartesian coordinates 5 5 and must convert this point to polar coordinates Recall that to find polar coordinates r 8 we use the following equations 2 x y 5 tan 8 We can use these equations to find the following values for x y 5 5 2 x y tan 8 y X y X 5

Differentiate Hint Use the Extended Power Rule g x In x 9 g x

Find the derivative with respect to x if f x 6x 12x 12 ex The derivative with respect to x if f x 6x 12x 12 ex is f x

Approximate to the nearest 0 1 degree all angles theta in the interval 0 degree 360 degree that satisfy the equation a sin theta 0 4530 b cos theta 0 9640 c tan theta 2 967 d cot theta 0 9405 e sec theta 1 419 f csc theta 1 588

IF bao lun 848 and Couluate 1 b lon 31 A The series will absolutly converge B Notenough informaler The series will Conditionally convere 5 The serves will

Find the length of the minor axis of an ellipse if the vertices are located at 5 7 and 5 3 and the foci are at 5 6 and 5 2 Thanks

Find and sketch the level curves f x y c on the same set of coordinate axes for the given values of c We refer to these level curves as a contour map 1 x y c 0 1 2 3 4 Choose the correct contour map below OA 00 1 OB OON e OC 6 Q G OD

Find the limit by rewriting the fraction first lim x y 1 1 lim x y 1 1 y x y x y x y III Type an exact answer

Which of the answer choices given below is equivalent to the following trigonometric expression 3 cos x Select the correct answer below A A W 00 6 O cos 2x cos 4x cos 4x cos 4x O cos 2x cos 4x O cos 2x 8 cos 2x

1 2 Find the dominant eigen value of the following matrix Show all your work T 3

With the aid of a power reducing formula 2sin acos a Select the correct answer below O cos 4a O cos 2a cos 4a O cos 4a cos 2a cos 4a

Use a power reducing formula to simplify 32sinacos a Write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1

If sin 0 13 and 0 is in Quadrant II then what is sin Simplify your answer completely Sorry that s incorrect Try again

Graph the function Then identify the domain range and y intercept and state whether the function is increasing or decreasing f x e 2x Graph the function Choose the correct graph below OA 12 06 2 O C 6 A 10 12 14 16 Ay 16 14 12 10 8 6 06 12 12 06 2 06 12 Q The function is 5 Q 5 The function s domain is Type your answer in interval notation Use integers or fractions for any numbers in the expression The function s range is Type your answer in interval notation Use integers or fractions for any numbers in the expression Identify the function s y intercept Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function s y intercept is Type an ordered pair OB The function has no y intercept CIES OB Ay 1 2 0 6 2 4 D 6 84 10 12 14 16 12 10 8 6 2 12 06 2 06 12 06 12 Q

Use a power reducing formula to simplify 16sin t Write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1

Which expression below can be obtained from 22sin a by using a power reducing formula Select the correct answer below 11cos 40 11cos 2a cos 40 11cos 20 cos 4c 11eos 2g 11cos 4a 33

Considering only the values of 0 for which sec 0cos 20 is defined sec 0cos 20 Select the correct answer below 2sin 0 tan 0 csc 0 2 O2 sec 0

For all values of a for which the expression is defined Select the correct answer below 2sin a 1 tan a 2tan a cos a sin a O2sin a tan a sec a 2tan a O tan 2a cos a

Calculate f 8x 6 dx given the following 7 7 7 8 7 x dx 93 1x dx 100 xcx 20 169 33 3 2 7 7 4 8x 6 dx

Find a power series representation for f x 3x 5 1 2x 3 For which values of x is it valid

Calculate 5x x dx given the following 9 9 5 5 x cx 804 3 10 Sx dx 271 3 9 5 5x x dx Type an integer or a simplified fraction xdx 28

6 Calculate 5x dx given the following 6 4 5 x dx 4 61 3 15x dx 0 2 6 2 Sx dx 5 91 3 5 9 xdx 1 2 4 4 Type an integer or a simplified fraction

Solve the given symbolic initial value problem y 6y 8y e s t 3 y 0 2 y 0 6 y t

Given that sin 0 213 and is in Quadrant II what is cos 20 2 13 Provide your answer below 20

Considering only the values of for which csc cos 23 is defined which of the following expressions is equivalent to csc cos 23 Select the correct answer below 2 O2 sec O2sin tan 2sin 6 O cor B 1

Considering only the values of for which Select the correct answer below 2tan cos B sin 2tan B 01 tan O cos sin cos 2B cos B is defined which of the following expressions is equivalent to cos s 2B cos B

Solve the second order equation xy 2y 8x by making the substitution u y 1 2 32 Cx 5x

2 Prove the Leibniz formula for n times differentiable functions f n fg n 1 f k g n k k k 0 where f k 0 k n is the kth derivative

Click here to watch the video Given the graph of y g x in the figure sketch the graph of each function and describe how it is obtained from the graph of y g x a y g x b y g x 5 c y g x d y g x 4 a Choose the correct graph of y g x below OA OOS OB M GYES a OD

Find the points of inflection of the graph of the function Order your answers from smallest to largest x then from smallest to largest y If an answer does not exist enter DNE f x 6x4 x x y x y Describe the concavity Enter your answers using interval notation If an answer does not exist enter DNE concave upward downward

y 3 cot 4x 1 Drag the movable black point to set the left vertical asymptote and shift the function the red point to set the right vertical asymptote thereby setting the period of the function and the blue point at the correct set of coordinates You may click or a point to verify its coordinates Note that the two asymptotes can be moved independently of each other and that only one period of the function is shown Provide your answer below 3TT 2 TT 5 4 3 2 1 1 72 0 0 1 2 3 4 1 2 0 TT 2 6 D 1 3TT 2

Find the extrema and points of inflection if any exist of the function Use a graphing utility to graph the function and confirm your results If an answer does not exist enter DNE f x x 1 e x x y minimum maximum point of inflection x y x y

Find a solution to y ke x 2 2 5x Hint dy xy 9x 5y 45 If necessary use k to denote an arbitrary constant dx help equations

Use implicit differentiation to find In xy 6x 35 dy dx dy dx

x 2 2 9 y 2 1 2 x 3 y 0 y 1 3 sqrt x 2 441 east one of the answers above is NOT correct dy X dx 9y point Solve the differential equation a Find an implicit solution and put your answer in the following form x 2 2 9y 2 2 constant help formulas Find the equation of the solution through the point x y 3 1 x 3y help equations x 9y 2 2 x 3y 0 y 2 441 Find the equation of the solution through the point x y 0 7 Your answer should be of the form y f x y 1 3sqrt x 2 441 help equations correct correc incorre

Use the Second Fundamental Theorem of Calculus to find F x dt ho 7 F x F x

1 point 1 t 2 16 dt At least one of the answers above is NOT correct 1 8 In x 4 x 4 y x 0 a Set up an integral for solving dy dx 1 8 plx 1 x 4 X t 0 1 x 16 when y 0 0 1 t 2 16 dt b Evaluate your answer to the previous part to find y x In 0 1 12 16 dt 4 x 4 CC C in

Consider the following function f x x 8x 7 a Find the critical numbers of f if any Enter your answers as a comma separated list X b Find the open intervals on which the function is increasing or decreasing Enter your answers using interval notation If an ans does not exist enter DNE increasing decreasing c Apply the First Derivative Test to identify all relative extrema If an answer does not exist enter DNE relative minimum x y relative maximum x y

The radius r of a circle is increasing at a rate of 7 centimeters per minute Find the rate of change of the area when r 35 centimet cm min

1 point Let S 1 represent the amount of a chemical reactant present at time t where i 20 Assume that S t can be determined by solving the initial value problem S aS K S and S 0 So where a K and So are positive constants Obtain an implicit solution of the initial value problem The differential equation often referred to as the Michaelis Menten equation arises in the study of biochemical reactions Enter the constant So as SO with a zero not the letter O help equations