Calculus Questions

Applying these values we get 1 x sin 4x cos 9x dx cos 5x cos 13x C

To find J x sin 4x2 cos 9x2 dx we can use formula 81 shown below cos a b u cos a b u 2 a b 2 a b sin au cos bu du Using this we have u a C and b

Find the volume generated when the region between the curves is rotated around the given axi Answer exactly x y and y x rotated around the line y 8

The following integral is a O b OC x cos x 2 ex dx Convergent using D C T by comparison to Divergent using D C T by comparison to 580 201 dx 8 S 1 dx Convergent by using D C T by comparison to 3 1 dx

Write a slope intercept equation for a line that passes through 7 0 and 5 3 The slope intercept equation for the line is Simplify your answer Use integers or fractions for any numbers in the equation

Use the Table of Integrals to evaluate the integral sin 20 V 5 3 sin 8 C de

Use the Table of Integrals to evaluate the integral 1 x dx x18 6 Part 1 of 5 The integral J dx x18 6 can be best matched by formula number from the Table of Integrals Hint Note that x18 9

Total profit is defined as total revenue R x minus total cost C x and is given by the function P x R x C x Given R x 60x 0 3x and C x 5x 13 find each of the following a P x b R 100 C 100 and P 100 P x Type in descending powers of x R 100 C 100 S P 100

Does correlation imply causation in the amount of hamburgers chicken cooked on the grill and the amour of propane gas used on the grill

Use the Table of Integrals to evaluate the integral 9 si 9 sin7 x cos x In sin x dx

Find an approximate value of the given trigonometric function by using the figure and a calculator sin 1 2 0 5 0 0 5 a the figure Round your answer to one decimal place b a calculator Round your answer to four decimal places

Evaluate F dr where is the line segment from 7 4 1 to 1 41 7 and 2 F yz cos xz 2x i sin xz 1 j xy cos xz 2z k

Ex 13 The order is for Zithromax PO 500 mg on day 1 then 250 mg qd on days 2 5 for a total dos of 1 5 g The label shows 200mg per 5 mL a How many should be given on day 1 b How many should be given on days 2 5 per day c Would the 30 ml size be large enough for the full course

A university is trying to determine what price to charge for tickets to football games At a price of 24 per ticket attendance averages 40 000 people per game Every decrease of 52 adds 10 000 people to the average number Every person at the game spends an average of 5 00 on concessions What price per ticket should be charged in order to maximize revenue How many people will attend at that price What is the price per ticket What is the average attendance people

Use the Table of Integrals to evaluate the integral 21 sin 21 sin x dx Enhanced Feedback C Please try again Try using substitution along with the integral Ju u sin u du 2u 1 sin 4

Find two values of 0 0 0 2 that satisfy the following equation 2 2 cos 0 0 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Uso a comm

Use the Table of Integrals to evaluate the integral 1 21 sin x dx X C

Write a polynomial f x that satisfies the given conditions 1 Polynomial of lowest degree with zeros of multiplicity 2 and multiplicity 1 and with 0 2 f 6 f x OC 2 3

Use the Table of Integrals to evaluate the integral Remember to use absolute values where appropriate 11 1 12 15 dy

Use the Table of Integrals to evaluate the integral 1 dx 9x 4 C

2 Explain the difference if any between a CD and DC b CD and DC c CD and DC d CD and DC

25 Suppose that points A R and V are collinear If AR 7 and RV 5 then which point cannot possibly lie between the other two

23 Suppose that planes M and N intersect point A lies in both planes M and N and point B lies in both planes M and N What can you conclude regarding AB

Substitution then gives us e98 sin 80 de C

298 sin 80 de we can use formula 98 shown below Je Using this we have a To find eau sin bu du eau a b a sin bu b cos bu C I b u 0 and du d0

The integral Tea e e sin 80 de can be best matched by formula number from the Table of Int

Sketch the region enclosed by y e5 y e7 and x 1 Find the area of the region

Find the volume of the solid generated by rotating the region bounded by y sin x and y 0 2 between 0 and about the x axis

Evaluate the definite integral 9 t4 In 2t dt 3 000 or 1170

A sketch of the region enclosed by y x and y 2 2 1 1 2 2 3x x 1 follows

Sketch the region enclosed by y 3x and y 5x Find the area of the region

The series Since 5 6n 7 the sequence the series then the series n 1 is most easily compared to 5 6n 7 5 6 72 5 6 7 v 5 6 12 and Select an answer 5 6 1 Select an answer by the Select an answer

If x S t 4t 2 dt 0 then f x 24 4 0 3 4x 3 2x X

Decide whether the series So Use a comparison test to a p series 1 k6 9k 5 k 1 k 1 converges diverges O 1 k6 9k 5 1 kp k converges where p

We want to use the Basic Comparison Test sometimes called the Direct Comparison Test or just the Comparison Test to determine if the series k converges or diverges by comparing it with 1 Ab We can conclude that The first series converges by comparison with the second series The Basic Comparison Test is inconclusive in this situation O The first series diverges by comparison with the second series

Given the series n 1 n 1 5 Does this series converge or diverge O diverges O converges If the series converges find the sup

Applying formula 69 now gives us the following Remember to use absolute values where appropriate Ita tan 16 x dx C

To find tan 16 x dx we can use formula 69 shown below tan u du tan u Inicos ul C To use this we ll let u Submit Skip you cannot come back Submit Answer and du dx

Tutorial Exercise Use the Table of Integrals to evaluate the integral Stan Part 1 of 4 tan 16 x dx

8 Suppose a population of bacteria is changing at a rate of dp 2 500 dt 1 0 25t where t is the time in days The initial population when t 0 is 2 000 Write an equation that gives the population at any time t a p t 10 0001n 1 0 25t 1 000 b p t ln 1 0 25t 2 000 c p t 2 500ln 1 0 25t 2 000 d p t 2 5001n 1 0 25t 1 000 e p t 10 0001n 1 0 25t 2 000

formula is a formula for calculating the solutions of a quadratic equation

A graph of y f x is shown In the same coordinate system sketch a graph of the derivative function y f x over the interval 4 4 4 3 2 1 4 3 2 1 1 2 3 2 3 Clear All Draw Line Segment Hint Start by finding where the derivative is equal to zero Then estimate the value of the derivative two units to the left and two units to the right of the vertex of the Make sure the height of your graph matches those values

The point P 1 3 lies on the function of f x 4x x If Q is the point x 4x x graph the function f x and the secant lines PQ passing through P 1 3 for each value of x below Also find the slope for each value Only a simplified fraction will be accepted If x 2 the slope of PQ is If x 1 5 the slope of PQ is If x 0 5 the slope of PQ is Graph 9 8 7 6 5 4 3 2

The graph of x 9y 5 0 crosses the y axis at y

Find an orthonormal basis for the solution space of the homogeneous system of linear equations x y z w 0 2x y z 2w 0 1 12

4 1 Find an expression for V v in terms of v 4 2 Find an expression for V 2 v 2 in terms of V 4 3 Use the result of 4 2 to deduce an expression for 2 whenever and V are orthogonal to each other

Suppose we declare the following 4 byte int int x 1122334455 and store this in memory location 0x100 on a little endian system What values would be stored in the following memory locations a 0x100 b 0x101 c 0x102 d 0x103

14 4 Evaluate the integral S x y z dz dy dx SS 0 0 0 SS S x y z dz dy dx 000 Type an integer or a simplified fraction

Describe the given region in polar coordinates such that 0 r and 0 0 2 The lower portion of the region is 0 rs The upper portion of the region is m 3

2 Find the area of the region cut from the first quadrant by the curve r 2 2 sin 20 A 0 Typo an oxnot