Calculus Questions

Let F x 1 f 3 dt Find F 4

Problem 6 Evaluate the following integrals a 3 2 b 6 S 5 72 dx 0 0 x 1 5x dx

Problem 3 The graph off is given to the right 1 Evaluate f x dx y f x 3 2 1 3 2 1 L 2 d 2

The graph of a function f is shown Which graph is an antiderivative of f DOO 0 2 y 2 0 1 5 0 0 5 0 5 1 0 b 0 2 0 4 0 6 0 8 X

A stone is dropped from the upper observation deck of a tower 400 m above the ground Assume g 9 8 m s a Find the distance in meters of the stone above ground at time t s t b How long does it take the stone to reach the ground Round your answer to two decimal places S c with what velocity does it strike the ground Round your answer to one decimal place m s d If the stone is thrown downward with a velocity of 5 m s how long does it take to reach the ground Round your answer to two decimal places

F 0 f 0 sec 0 tan 8 9e Need Help Submit Answer 0 11 Points Read It DETAILS SCALCET9 4 XP 9 012 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative

A company estimates that the marginal cost in dollars per item of producing x items is 1 67 0 002x If the cost of produci one item is 552 find the cost in dollars of producing 100 items Round your answer to two decimal places

Find f f t f t 2 cos t sec t n 2 t 2 f 3 3

Find the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative F x f x x 5 5x 15

Since raindrops grow as they fall their surface area increases and therefore the resistance to their falling increases A raindrop has an initial downward velocity of 10 m s and its downward acceleration is a 19 0 9t if 0 st 10 10 if t 10 If the raindrop is initially 500 m above the ground how long in seconds does it take to fall Round your answer to two decimal places S

Find a function f such that f x f x 2x3 and the line 2x y 0 is tangent to the graph of f

Find f f t 3 f 4 11 f 4

A car braked with a constant deceleration of 40 ft s2 producing skid marks measuring 80 ft before coming to a stop How fast ft s was the car traveling when the brakes were first applied ft s

Find the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative F x f x 2x4 5x x X 0

Consider the following problem a box with an open top is to be constructed from a square piece of cardboard 3 feet wide by cutting out a square from each of the four corners and bending up the sides Find the largest volume that such a box can have a Draw several diagrams to illustrate the situation some short boxes with large bases and some tall boxes with small base Find the volume of each configuration Does it appear that there is a maximum volume If so estimate it b Draw a diagram illustrating the general situation Let x denote the length of the side of the square being cut out Let y denote the length of the base c Write an expression for the volume V in terms of both x and y V d Use the given information to write an equation that relates the variables x and y e Use part d to write the volume as a function of only x V x f Finish solving the problem by finding the largest volume in ft that such a box can have V

A box with a square base and open top must have a volume of 13 500 cm Find the dimensions of the box in cm that minimiz the amount of material used sides of base height cm cm

A steel pipe is being carried down a hallway that is 9 ft wide At the end of the hall there is a right angled turn into a narrowe hallway 6 ft wide What is the length of the longest pipe in ft that can be carried horizontally around the corner Round yo answer one decimal place ft 0 6

Find the equation of the line through the point 2 5 that cuts off the least area from the first quadrant

A manufacturer has been selling 1 000 flat screen TVs a week at 500 each A market survey indicates that for each 10 rebate offered to the buyer the number of TVs sold will increase by 100 per week a Find the demand function price p as a function of units sold x p x b How large a rebate in dollars should the company offer the buyer in order to maximize its revenue c If its weekly cost function is C x 64 000 120x how should the manufacturer set the size of the rebate in dollars in order to maximize its profit

What is the maximum vertical distance between the line y x 2 and the parabola y x for 1 x 2

If you are offered one slice from a round pizza in other words a sector of a circle and the slice must have a perimeter of 36 inches what diameter pizza in inches will reward you with the largest slice in

If 30 000 cm of material is available to make a box with a square base and an open top find the largest possible volume in cm of the box cm

Find the area of the largest rectangle that can be inscribed in the ellipse 1

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm If the area of printed material the poster is fixed at 1 536 cm2 find the dimensions in cm of the poster with the smallest area width cm 121

at d its to point pposite A B the other side of the lake in the shortest possible time see the figure She can walk at the rate of 4 mi h and row a boat at 2 mi h For what value of the angle shown in the figure will she minimize her travel time G 11 A 0 2 B 2 C

Find the area of the largest rectangle that can be inscribed in the ellipse 1

Find the dimensions of a rectangle in m with perimeter 76 m whose area is as large as possible Enter the dimensions as a comma separated list m

At time t the position of a body moving along the s axis is s t 9t 24t m a Find the body s acceleration each time the velocity is zero b Find the body s speed each time the acceleration is zero c Find the total distance traveled by the body from t 0 to t 3 a What is the body s acceleration each time the velocity is zero Select the correct choice below and if necessary fill in the answer box to complete your choice OA m s2 Simplify your answer Use a comma to separate answers as needed OB There is no solution b What is the body s speed each time the acceleration is zero Select the correct choice below and if necessary fill in the answer box to complete your choice OA m s Simplify your answer Use a comma to separate answers as needed OB There is no solution c What is the total distance traveled by the body from t 0 to t 3 m Simplify your answer CL

Find the value of each variable b b 9 2 and d 45 C a d b c Simplify your answers Type exact answers using radicals as needed 30

Write an equation of the line containing the given point and parallel to the given line Express your answer in the form y mx b 2 6 5x 9y 2 The equation of the line is y Simplify your answer Use integers or fractions for any numbers in the expression

X Simplify your answer Type an exact answer using radicals as needed

Evaluate Be sure to check by differentiating 1 6 3x dx 6 3x dx x 2 xi 16 3x dx 0 Type an exact answer Ilse paronth

Evaluate Be sure to check by differentiating 1 6 3x dx dx x 2 6 3x dx Tyne an exo opou

Suppose the charge q on a capacitor is given by q 2 95 C e t 0 220 s a Find the value of q when t 0 0380 s C b Find the value of t when q 1 12 C

xin x3 A In In x3 C B In x C in 0 D in inx 3

xin x3 A In In x c C B In x C C in x C D in In x

Evaluate Be sure to check by differentiating In x 29 X In x 29 dx x 0 dx X Type an exact answer Use parenthopon to

The figure below is a contour diagram of f x y In each of the following cases list the marked points in the diagram there may be none or more than one at which a 0 b f 0 C C c 0 O ogress 0

Find the critical point s of f x y f x y x 3y 12x 6y 3 f x y has Choose one critical point s

Calculate all four second order partial derivatives of the function 3x f x y y 0 and confirm that the mixed partials are equal Y fax x y fay x y

Calculate all four second order partial derivatives of the function f x y 9xe and confirm that fry fyr Assume the variables are restricted to a domain on which the function is defined fxx fay fyx fam

Condense the left hand side into a single logarithm Then solve the resulting equation for A log x log y 3 log z log 4 A 1 help formulas

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 B k uxv x uxw C kvxw OD k uxv xw f Which of the following describes a vector of length u in the direction of v OA V ul OB lul Oc lulv A

Given honzero 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 d Which of the following describes the volume of the parallelepiped determined by u v and w A vxu w B uxv w C D e If k is any constant which of the following describes a vector orthogonal to u xv and uxw u v xw uxv w OA k uxv uxw B k uxv x uxw OC Kvxw OP kluxv xw

Find the length and direction when defined of u xv and vxu u 8i 3j 5k v 4i 4j 2k uxv 6 17 Type an exact answer using radicals as needed Select the correct choice and fill in any answer boxes in your choice below A 7 3 17 2 3 17 Type exact answers using radicals as needed The direction of u x v is OB The direction of u xv is undefined i j vxu Type an exact answer using radicals as needed 10 3 17 k

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 OB O D Vou V V U V V V vou u u u u b If k is any constant which of the following describes a vector orthogonal to u and v OA ku v V OB kuxv OC kluxv

Find the length and direction when defined of u xv and vxu u 8i 3j 5k v 4i 4j 2k luxv 6 17 Type an exact answer using radicals as needed Select the correct choice and fill in any answer boxes in your choice below A The direction of u x v is 14 i 4 Type exact answers using radicals as needed OB The direction of u xv is undefined 20 k

Find the volume of the parallelepiped box determined by u v and v u 2i j Simplify vo V for 4i j 2k The volume of the parallelepiped is 4 units cubed W i 2k

What is the energy in joules of one photon of microwave radiation with a wavelength 0 122 m O 1 63 x 10 24 J 4 07 x 10 10 J O 2 70 x 10 43 J 5 43 x 10 33 J

Find the length and direction when defined of u xv and vxu u 8i 3j 5k v 4i 4j 2k luxv Type an exact answer using radicals as needed