Calculus Questions

Evaluate the integral 2 sec 4 ec 30 de 4 2 sec 30 d0

Evaluate the integral 3 sin x dx sin x dx

In each part determine all values of p for which the integral is improper Enter in interval notation or none if there are no relevant values of p dx 0 dat 0 XP p values that make integral improper dx x p p values that make integral improper b c S dr

Use any method to evaluate the integral cot 4x sec 4x cot 4x sec 4x dx dx 0

Evaluate the integral 2 cos 5x dx 3 2 cos 5x dx 3

Evaluate the integral T S 2 3 70 sin 4x cos x dx I S 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expi 70 sin x cos x dx 4

Evaluate the integral Scos 3 cosx sin xdx 3 cos cosx sin xdx

Evaluate the integrals that converge enter DNC if integral Does Not Converge S 0 8 x da

Find the indicated integral if it exists 8 e8x el6x 1 dx

Box Office Receipts The total worldwide box office receipts for a long running movie are approximated by the following function where 7 x is measured in millions of dollars and x is the number of years since the movie s release T x 120x x 4 How fast are the total receipts changing 1 yr 4 yr and 6 yr after its release Round your answers to two decimal places after 1 yr 38 40 million year after 4 yr after 6 yr S million year million year

Use L H pital s Rule possibly more than once to evaluate the following limit 102 112 lim 818 NE in the blank

A polynomial function has 3 real zeros and 4 non real zeros One of the real zeros has a multiplicity of 6 What is the degree of the polynomial 1 A 7 B 9 C 12 D 13

Apply L H pital s Rule to evaluate the following limit It may be necessary to apply it more than once 5x 5 x 7 2 lim

4 No calc The x coordinate of the point where the line tangent to the parabola y 8x at 2 4 intersects the axis of symmetry of the parabola is x A 1 B 1 C 2 D 0 5 No calc If y 3sin x 4 cos x then y y A 6sin x 8 cos x B 6sin x 8 cos x C 6sinx 8cos x D 6sin x 8 cos x E 0 6 Calc Let f be the function given by f x tan x and let g be the function given by g x x At what value of x in the interval 0 x do the graphs off and g have parallel tangent lines A 0 B 0 660 7 No calc The lim A40 A 1 C 2 083 h 8 No cale lim A 4 D 2 194 at x 3 is B 0 1 D 3 lim 1370 13 0 h 70 x 16x 20x 4x B 2 I m 0 0 0 0 E 2 5 D 2 E 2 207 E DNE E 4

Find a polynomial f x of degree 4 with real coefficients and the following zeros 1 multiplicity 2 1 2i To

Solve the following inequality x 6 312 0 0 x 5 Write your answer using interval notation 0 0 0 0 0 0 0 0 8 8 QUD

Divide 10 13x 8x 2x 4 Write your answer in the following form Quotient 10 13x 8x 2x 4 0 0 2x 4 Remainder 2x 4 15

The graphs of f and g are given Find a formula for the function g g x 5 an g y 5 5 f x x 50 X

A function f is given and the indicated transformation is applied to its graph Write the equation for the final transformed graph f x x shift 2 units to the left

A function f is given and the indicated transformations are applied to its graph in the given order Write the equation for the final transformed graph f x x reflect in the y axis and shift upward 7 units y

16 A stone is dropped into a lake creating a circular ripple that travels outward at a speed of 60 cm s Find the rate at which the area within the circle is increasing after a 1 s b 3 s and c 5 s What can you conclude

3 Use the graphs of f and g to find the domain of the function indicated a f g b f g c fog 2 f x 4 Figure 1 Graph of f x and g x g x

1 Calculate each of the following and simplify your answer f g fg fog go f a f x x and g x 1 b f x x and g x x 1 X x x 1

Therefore the anti derivative of Question 4 Answer The anti derivative of It is known that d ax b 30 ax b 1 d ar b 30 de x b x b Therefore the anti derivative of Question 5 sin 2x 4e Answer The anti derivative of sin 2x 46 It is known that Class XII de Question 6 is the function of x whose derivative is Answer 4 fe de fide sin 2x 4e Therefore the anti derivative of sin 2x 4e is is the function of x whose derivative is Page 2 of 216 Chapter 7 Integrals of sin 2x 40 con 2x is Maths

104 If lim f x 4 and lim g x 5 find lim 2f x g x

For the following quadratic function defined a use vertex formula to find the coordinates of the vertex a graph the function P x 4x 40x 98 AWN The vertex of the quadratic function is Type an ordered pair

A quantity P is an exponential function of timer such that P 170 when t 4 and P 150 when information about P Poe to a Find values for the parameters k and Po Round your answers to three decimal places k P per unit time b Give the initial quantity and the continuous percent rate of growth or decay Round your answer for the initial quantity to three decimal places Enter your answer for the growth or decay rate as a positive value rounded to one decimal place The initial quantity is i and the quantity is 2 Use the given at a continuous rate of

The figure shows the graph of a quadratic function f x Use it to find the minimum value of f x y f x 8 8 Ay 201 18 16 14 12 10 964GJ 6964 8 2 14 1210 8 6 4 2 2 4 6 8 101214 X Q Q The minimum v Type an intege

5 Y1 is defined as a quadratic function Determine the coordinates of the vertex of the graph maximum or minimum point and value and the range of the function ww The coordinates of the vertex are Type an ordered pair 1 7 X 1 X E 10 34301 5 5

ertex and b the x intercepts y 0 29x 7x 0 37 a The vertex is Type an ordered pair Round the final answer to the nearest hundredth as needed Round all intermedia vo decimal places as needed

or the following quadratic function a use the rmula to find the coordinates of the vertex an e function x x 4x 1 he vertex is Type an ordered pair

Tell whether a linear or quadratic function would be a more appropriate model for this set of graphed data If linear tell whether the slope should be positive or negative If quadratic tell whether the coefficient of x should be positive or negative 40 O Would an appropria data be linear or qu Linear Quadratic ho x Should the coefficier or negative ONegative Positive

4 Given the function f x what is the value of a f 2 b f 5 c f f 2

figure shows the graph of a quadratic function y f x AY 20 y f x 16 12 8 16 4 12 4 8 12 16 Q How many real solutions are there f x 1 Choose the correct answer below OA One OB Two OC None

y x 1 1 The whether its graph opens upward or downw Select the correct choice below and fill in the answer box to complete your choice Type an ordered pair OA The vertex of the parabola is OB The vertex of the parabola is and it opens downward and it opens upward

e quadratic function defined a write the function in m P x a x h k b give the vertex of rabola and c graph the function x 2x 7 plify your answer Use integers or fractions for any bers in the expression 516 7 512

have real solutions tell whether they are rational or irrational Do not actually solve the equation 9x 18x 9 0 VYRIGHT OF Tiny is TO CUTTOULOTTUVIL VI I qyuuurucu vyuuuvIICIA b 4ac b b 4ac b b 4ac b 4ac The discriminant is 0 Simplify your answer Type an integer or a simplified fraction Determine the number of real solutions of the equation If the equation does have real solutions tell whether they are rational or irrational Select the correct choice below and if necessary fill in the answer box to complete your choice OA The equation has B The equation has OC The equation has no real solutions UAL UI real rational solution s Type a whole number real irrational solution s Type a whole number

Find a possible formula for the function represented by the data X 0 1 2 3 f x 4 80 6 72 9 41 13 17 NOTE The value for the base should be correct to one decimal place f x

For y 2x 10x d y 0 6x find 445

A town has a population of 4791 people at time t 0 The population increases by 3 per year Enter a formula for the population P of the town as a function of year t P t

4 Given this graph of the function f x Find a f 4 e x when f x 2 b f 0 1 x f x when f x 0 c f 3 d f 5

The gross domestic product G of Switzerland was 685 4 billion dollars in 2013 Give a formula for G in billions of dollars t years after 2013 if G increases by a 4 per year G t b 6 billion dollars per year G t

Give a possible formula for the function shown in the figure below y 20 NOTE Round any calculated values to two decimal places y t 20 25 11 30 t

4 g a a 1 h a 3a 4 Find 2 AX

The graph of f is given State with reasons the num bers at which f is not differentiable 35 2 0 fr X 4

Use a calculator to evaluate the trigonometric function Round your answer to four decimal places Be sure the calculator is in the correct moc sin 330

5 4 3 2 1 5 4 3 2 1 7 2 3 5 4 2 3 4 List all the numbers x at which the function graphed above is not differentiable Separa commas

6 Let f x 5x x f x 65x x 2 Question Help 5 35 4 2x x Video X

If f x 2 x x 5 x 3 find f x 2 1 x 5 x 3 2 x 3x 3 Find f 1 1 5 2 x X

2 A particle moves with position function s t4 4t 20t 20t t 0 a At what time does the particle have a velocity of 20 m b At what time is the acceleration 0 What is the significance of this value of t