Application of derivatives Questions and Answers

Which of the expressions HO 1 D I ve III II are always even if a and b are distinct positive even natural numbers Only B a b 4 a b 2 III ab E II ve III C I ve II

2 8 2 2 2 0 2 A X If the addition subtraction and multiplication x symbols are placed in the empty boxes in the expression in which order will the result of the operation be the smallest D X B x 2 E X C X

3 Find eigenvalues and eigenfunctions of the boundary value problem z y Xy y 1 0 y 2 0

1 Prove that the following identity is wrong Z 1 x dx In x C Hint Come up with a function that is not of the form In x C but its derivative is still 1 x

Find the Radon Transform sinusoidal sine wave graph for coordinate 3 5

Graph the exponential function y 3x

Find the function s relative maxima relative minima and saddle points if they exist If an answer does not exist enter DNE z 18 x xy y 21y x y z elative maximum elative minimum addle point x y z x y z

Use the Cramer s rule to solve the system of equations given below 4x y 23 4x9y 15 compli

A market has an inverse supply function and an inverse demand function given by q 1 2q p q 6 3q espectively A percentage of the price tax of 100r is imposed on the market Find the equilibrium price p O a Ob O c O d O e 15 5 3r 5 5 3r 10 5 3r 1 5 3r 30 5 3r

write the points that the graph on the dont exis

T Use the half angle formulas to find the exact value of the trigonometric function tan 12 Find the exact value of the expression K tan 12 Type an exact answer using radicals as needed Rationalize the denominator as needed

Use the figure to find the exact value of the following trigonometric function tan 29 tan 28 Simplify your answer 20 17 15 B

19 A 2 0 1 1 3 2 B 299 1 2 2 3 2pril 021 01 E

Use reference angles to find an arbitrary angle for the tan 240 degrees a 120 b 60 c 330 d 18

5 For what angles x in 0 2rt does the cos x have the same value as sin 5m 4T 5T 3 a 3 b C d 117

5 What type of conic section is the given equation 3x 4y 4y 6x 12 0 b parabola c ellipse a circle d hyperbola

4 Convert the point from polar form to rectangular form 5 75 a 2 34 2 38 b 2 38 2 34 c 1 29 4 8 d 1 29 4 8

A pot of tea is heated to is poured into a mug and taken outside where the temperature is 18 C After 2 minutes the temperature of the cup of tea is approximately 65 C Use Newton s Law of Cooling to determine the value of the decay constant k correct to 3 decimal places T t Ta To Ta e kt Ta temperature of the surrounding air To initial temperature t time

35 Solve for x 4 1 A 30 B 30 C 6 D 6 8x 10

40 Find the common difference in the arithmetic sequence 2 7 12 17 22 A 11 B 5 C 5 D 10

48 Find the solution set of this equation x 3x x 1 A 1 B 2 C 3 D 2 1

x 2y 4 36 Find the solution set of this linear system 3x y 2 A 2 0 B 0 2 C no solution D 0 2

42 Use a geometric series to find the rational number represented by the decimal 54 What does the rational number equal 59 6 B 11 C 27 50

37 Find the first 5 terms of this sequence an n 3 A 1 2 3 4 5 B 2 1 6 13 22 C 2 1 3 5 7 D 3 2 1 5 10

x y 2 29 Which shows the graphs of the equations x y 0 A B C D I

31 Write 3 loga 4 loga 7 as a single logarit A loga 448 B loga 84 12 N C loga 7 D Joga 64 7 I

12 342 Evaluate the determinant 1 1 A 19 B 19 C 5 D 5 201

18 Solve for x 9x 3x 6 A 4 B 3 C 6

A helicopter hovers 1100 feet above a small island The figure shows that the angle of depression from the helicopter to point P on the coast is 32 How far off the coast to the nearest foot is the island The island is approximately feet off the coast Simplify your answer Round to the nearest whole number as needed 1100 ft 32

Graph the rational function x 10x 2 2x 4 Start by drawing the asymptotes Then plot two points on each piece of the graph Finally click on the graph a function buttor 1 X 0 Start over

Given the function below f x find the following a f 3 Select b f 1 Select c f 2 Select 2 0 1 5 x d f 3 Select 1 x 2 x 2 2 x 2 x 2

Find all solutions to the equation below log 3x 2 log3 x log2 x 2 1 x 6 is the only solution There is no solution x 1 or x 6 Ox 1 is only solution

Consider the integral 2 x x 1 da In the following we will evaluate the integral using two methods A First rewrite the integral by multiplying out the integrand 2 x x 1 dx s Then evaluate the resulting integral term by term 22 2 x x 1 dx B Next rewrite the integral using the substitution w 2 x x 1 dx 23 2 1 da dw Evaluate this integral and back substitute for w to find the value of the original integral 2 x x 1 dx C How are your expressions from parts A and B different What is the difference between the two answer from B answer from A Are both of the answers correct

The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases Here is a possible model C q 4 800 919 where q is the reduction in emissions in pounds of pollutant per day and C is the daily cost to the firm in dollars of this reduction What level of reduction corresponds to the lowest average cost per pound of pollutant Round your answer to two decimal places pounds of pollutant per day What would be the resulting average cost to the nearest dollar per pound

find area of surface generated by reviving th curv sin t X y 1 cos t 0 t 2 x axis 6 2 b 4 c 1T

Solve the following Equations for 0 0 360 1 sin 2x sinx 0 2 cos 0 sin 0 0

Find the y intercept of the polynomial function 7 f x x 2x 3 A 0 B 1 C 3 D 3

Find the composite function for the given functions 2 fg for f x 7x 12 and g x 4x 1 A 28x 5 B 28x 47 C 28x 11 D 28x

Let g x 173x cos 21x Use the 2nd derivative to determine whether the graph of g is concave up or concave down at the point where x 0 12 O Concave up O Concave down O There is an inflection point at x 0 12 O The graph has no concavity

Suppose you were to use calculus techniques i e those from the lecture 22 notes to find the absolute extreme values of g x 8x x on the interval 2 1 Which of these function values would be required in order for you to draw your conclusions O g 2 g 2 g 1 and no other values O g 2 and no other values Og 2 g 1 g 0 g 1 and no other values O g 2 g 1 and no other values

An object is falling in such a way that its height in feet after t seconds is given by s t 16t 64t 80 What is the object s velocity in feet per second when it hits the ground Write your exact numerical answer in the box below

1 Find the critical number s of the function f x x O 0 and x Ox and x 0 x 0 O There are no critical numbers

3 Sketch the graph of a function f for which f 0 0 40 3 f 1 0 f z 1

Let h x x g x Given the following information compute h 3 g 9 7 g 9 3 g 3 5 g 3 8 g 2 4 g 2 9 Write your exact numerical answer in the box below

8 Given f x y ex y Let P 4 2 u 1 4 a Find the gradient of f at P b Find the maximum value of the directional derivative at P c Find the directional derivative of f at P in the direction of u

5 Find the equation of the tangent line to the curve at the specified value of the parameter x 1 3 3t 5t y t t 4 at t 1 3

8 Find the equation of variation given x varies directly as y and x 15 when y 2

Solving a right triangle means finding the missing length s of its and the measurement s of its legs sides angles

r 1 sin 1 S 4 w 2 of 5 24 to 7 40 1 2 d 7 5 O S 3 d

50 How much interest is generated by investing 7000 compounded continuously for 3 years at 2 5 annual interest