# Calculus Questions

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Application of derivatives
Solve for the specified variable n q y for n n HIE Type an exact answer using radicals as needed Calculus
Application of derivatives
r X 1 0 The solution set is 0 Type an exact answer using Express complex numbers in integers or fractions for any r expression Use a comma to as needed Calculus
Application of derivatives
Evaluate the discriminant and use it to determine the number of real solutions of the equation If the equati have real solutions tell whether they are rational or irrational Do not actually solve the equation 9x 18x 9 0 www Which of the following is the correct formula for the discriminant of the quadratic equation ax bx c 0 O b b 4ac O b 4ac O b b 4ac O b 4ac Calculus
Differentiation
Solve the following equation For an equation with real solutions support your answer graphically x 81 The solution set is Use a comma to separate answers Express complex numbers in terms of i Calculus
Application of derivatives
ve the following equation For an equation with a real solution support your answers gr 4 9x 2x 0 EER e solution set is ype an integer or a simplified fraction Use a comma to separate answers as needed Calculus
Application of derivatives
K equation FO an equation with real solutions support the answe x 8x 9 Rewrite the equation in factored form 0 0 Factor completely Calculus
Application of derivatives
3x 21 quation For an eq ition with real utions support your answer graphicall he solution set is Type an exact answer using radicals as needed Use a comma to separate answers as needed E umbers in terms of Calculus
Differentiation Calculus
Indefinite Integration
For the given complex number a state the real part b state the Imaginary part and pure imaginary or nonreal complex 2 9i a What is the real part of 2 9i 2 b What is the imaginary part of 2 9i 9 c Identify the number 2 9i Select all that apply A pure imaginary B nonreal complex C real y the nu Calculus
Application of derivatives
10 If a ball is thrown vertically upward with a velocity of 80 ft s then its height after t seconds is s 80t 16t2 a What is the maximum height reached by the ball b What is the velocity of the ball when it is 96 ft above the ground on its way up On its way down Calculus
Limits & Continuity
5 Graphs of the velocity functions of two particles are shown where t is measured in seconds When is each particle speeding up When is it slowing down Explain a b VA VA 0 1 0 1 Calculus
Application of derivatives
16000 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 5000 4000 5 FA 10 15 20 25 A quadratic model C t for the cost of tuition at a small private college in dollars for t years since 1990 is C t 8 28t 269 05t 3500 Find the equation of the tangent line for tuition in 2017 y mt b where m The tangent line estimate for tuition in 2017 is and b n M Calculus
Differentiation
DETAILS 07 A ladder that is 15 feet long leans against the side of a house The angle of elevation of the ladder is 80 Find the height from the top of the ladder one decimal place ft the ground Round your dis Calculus
Indefinite Integration
Suppose f 5 9 and f 5 2 1 The equation of the tangent line of f at 5 is t x 2 Approximate f 5 46 to the nearest 2 decimal places f 5 46 A Calculus
Application of derivatives
Find the exact values of the remaining trigonometric functions of satisfying the given conditions If an answer is undefined enter UNDEFINED 24 25 tan 0 0 sin 8 tan 8 csc 8 sec 8 cot 8 Cos 0 7 25 7 24 25 7 25 24 24 7 Calculus
Vector Calculus
Use the Law of Cosines to solve the triangle Round your answers to two decimal places A B C b 4 A O O O C C 8 a 7 B Calculus
Application of derivatives
Suppose is a continuous function where f 10 6 and f 10 3 The equation of the line tangent to the graph of y f x at x 10 will be y So f x Based on this f 10 8 A solution to f x 0 is a for a close to a 10 Calculus
Application of derivatives
Suppose f is a function with 7 30 and f 7 3 Using the local linearization L x at x 7 estimate the following values of f f 10 L 10 f 6 f 6 5 Samotne Calculus
Differential equations
Let f x We wish to use linear approximation to approximate the values of f x when is close to 36 At x 36 what point is on the graph of f x Point At Jumanni Comm Slope 36 what is the slope of the tangent line to f x Calculus
Indefinite Integration Calculus
Application of derivatives
5 4 3 2 5 Add Work 4 3 2 3 5 to In the above graph estimate the slope of the tangent line at x 4 Calculus
Differentiation
Use the Law of Sines to solve if possible the triangle If two solutions exist find both Round your answers to two decimal places If a triangle is not possible enter IMPOSSIBLE in each corresponding answer blank A 79 a 14 b 15 B C Calculus
Differentiation
An airplane flies at an altitude of 6 miles toward a point directly over an observer Consider 0 and x as shown in the figure To a Write 8 as a function of x 8 0 6 mi b Find 8 when x 14 miles and x 7 miles Round your answers to one decimal place x 14 miles 8 x 7 miles 0 O Not drawn to scale Calculus
Vector Calculus
Solve the right triangle shown in the figure for all unknown sides and angles Round your answers to two decimal places B 76 6 a 4 8 A C b C B a C O O b A Calculus
Application of derivatives
Evaluate the sine cosine and tangent of the angle without using a calculator If an answer is undefined enter UNDEFINED 57 3 sin 8 cos 8 tan 8 Calculus
Application of derivatives
Evaluate the sine cosine and tangent of the angle without using a calculator If an answer is undefined enter UNDEFINED 300 sin 8 cos 8 tan 8 Calculus
Limits & Continuity
Come up with an algebraic expression for a function with exactly two discontinuities It can contain familiar functions and it can be a piecewise function Your task will be to find the discontinuities in another team s function Answer Calculus
Indefinite Integration
er leans against the side of a house How far is the bottom of the ladder from the side of the house when the angle of elevation answer to the nearest tenth 69 0 X Calculus
Application of derivatives
Find all k such that g x k Answer x 2x x 2 if x 2 if x 2 is continuous Calculus
Vector Calculus
Find x the angle of depression from the top of a lighthouse that is 190 ft above water level to the waterline of a ship 935 ft off shore Round your answer to the nearest tenth of a degree x 935 U 190 0 X Calculus
Vector Calculus
Jenny and Jim are standing on a riverbank at points A and B respectively See the figure below Jim is 160 meters from a house located across the river at point C Suppose that angle A angle BAC is 41 and angle B angle ABC is 73 How far are Jenny and Jim standing from one another Round your answer to the nearest tenth of a meter 4 0 meters X Calculus
Application of derivatives
A pilot is flying over the ocean She determines that the angles of depression to two ships are 52 and 45 as shown in the figure below The plane is 2 miles from the ship located at point 4 How far apart are the ships Round your answer to the nearest tenth of a mile 2 mi B miles X Calculus
Definite Integrals
Evaluate the integral In 15x St 3 X In 15x 3 dx dx Calculus
Application of derivatives
avi and Carmen are standing on a riverbank at points A and B respectively See the figure below Carmen is 180 meters from a house located across the ver at point C Suppose that angle A angle BAC is 55 and angle B angle ABC is 73 How far are Ravi and Carmen standing from one another Round our answer to the nearest tenth of a meter 55 44 73 180 10 1 meters X Calculus
Application of derivatives
Find the following limit x 16 8 lim x 4 x 4 Calculus
Application of derivatives
Use the sign chart for y f x below to determine where f x 0 f x I 4 Choose all that apply 0 3 00 3 0 0 1 1 0 4 4 1 0 1 1 1 3 0 4 1 O 1 3 Und 1 13 110 Und 3 Calculus
Differentiation
ountain officials want to build a new ski lift from B to C as shown in the figure below The distance from A to C is 1530 feet They measure angle DAC to be and angle DBC to be 20 What is the distance from A to B Round your answer to the nearest tenth of a foot 1530 ft 40 A 20 feet Calculus
Differentiation
What is the first derivative of f z ln 42 3z 5 Calculus
Indefinite Integration
Consider a triangle ABC like the one below Suppose that B 58 C 67 and a 30 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or A 0 b 0 c 0 or O X No solution Calculus
Application of derivatives
Determine the derivative of f z 2e 1 Calculus
Application of derivatives
Determine the derivative of f x 1 5 Calculus
Vector Calculus
sketch the triangle O LA 50 25 73 c 270 O 2C 57 B B 270 73 73 270 50 50 C A O A A Solve the triangle using the Law of Sines Round side lengths to the nearest Integer a 208 962 x b 175 34 50 50 270 270 73 73 B B Calculus
Vector Calculus
To find the distance across a river a surveyor chooses points A and B which are x 350 ft apart on one side of the river see the figure She then chooses a reference point C on th opposite side of the river and finds that ZBAC 82 and ZABC 52 Approximate the distance from A to C Round your answer to the nearest foot X ft A x ft 82 52 B Calculus
Application of derivatives
Consider a triangle ABC like the one below Suppose that A 112 B 36 and c 60 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or C a b 0 or X No solution Calculus
Application of derivatives
Use the Law of Sines to solve for all possible triangles that satisfy the given conditions If an answer does not exist enter DNE Round your answers to one decimal place Below enter yo answers so that ZA is smaller than ZA b 27 c 38 ZA ZC a ZB 22 0 x X x ZA 4C a2 X X x Calculus
Differentiation
Use the Law of Sines to solve for all possible triangles that satisfy the given conditions If an answer does not exist enter DNE Round your answers to one decimal place a 50 b 108 ZA 55 ZB ZC C 0 X X x Calculus
Application of derivatives
Determine the derivative of the function f x 225 3e6e Calculus
Limits & Continuity
f x x 3 2 x 3 x 3 x 3 1 Evaluate f 3 in the piecewise function above Type a response Calculus
Differentiation
3 f x x Use the shifts and scalings to transform the graph of f x x into g x 2 x You need to describe each transformation step and draw the curve transform 1 transform 2 transform 3 g x 2 x 1 Calculus
Definite Integrals
5 points and the trigonometric expression cos 2 2 A u can t use a calculator where 0 A F