Calculus Questions

12 g x 2 x 25 A 8 x 5 B g x 2x 3 25 2 C g x D g x 6 4x 3 2 13 g x 4 3x 2 A g x 12 x 4 B g x 2x 4 3 C g x 25 2x 5 D g x 2 2

18 x 2x 24 x 5 A x 3 9 x 5 4 B x 3 C x 3 D x 3 x 5 4 x 5 6 x 5 19 5x 30x 12 x 6 5 A 5x x 6 12 x 6 C 5x 9 x 6 9 x 6 B 5x D 5x

20 3x 13x13x 16x 5 x 5 1 A 3 2x 3x 1 B 3x 2r 3x 1 x 5 C 3x 2x 3x 1 10 x 5 4 x 5 D 3x 2x 3x 1 10 x 5

Find the inverse of each function 10 S x A x Sx B 4 C x 5 6x 5 D x 2x 6 f x 16 x 11 g x 2r 8 A g x 5 2 B g x 2 x C g x x 3 2 D g x 4 x

State if the given functions are inverses 10 x 2 5 g x s x x 2 A No B Yes 6 S x x 2 8 x A No 2 3 B Yes

Which of the following sets are subspaces of R OA 7x 4y 5x 9y 6x 9y x y arbitrary numbers OB x x 2 x 8 x arbitrary number c x y z 2x 8y 3z 0 D x y z x y z OE x y z x y z 7 A

Do 4 The natatorium pool is 25 0 meters by 25 0 yards Assuming the pool is uniformly 396 cm deep what is the volume of the pool in liters 2 26x10 liters 2 0 LICE

Consider the curve given by the parametric equations a Determine the point on the curve where the tangent is horizontal t x t t 147 y 2 t 147 b Determine the points t t2 where the tangent is vertical and t t t

Do 3 Determine the number of grams in the following A 15 85 moles of Helium 63 45gte 142atte 1 th

B 71 60 g Si 2 549 mores Si 28 085951 71 600 Spo mole si

Evaluate the indefinite integral given below Provide your answer below 8 36x sec 3x 2x tan 3x 2x dx 8 36x sec 3x 2x tan 3x 2x dx

1 point Find the equation for the line tangent to the parametric curve Y X y at the points where t 4 and t 4 For t 4 the tangent line in form y mx b is y For t 4 the tangent line is t 16t 16t 14

1 point dy dx parameter Find and d at the given point without eliminating the dx X dy dx t 6 y t t t 2 d y dx

21 Find the exact values of the three trigonometric functions sine cosine tangent of the real number t a b a D 5 13

1 point Find the exact length of the curve given by 1 t 3 Length X 2t y 0 t 1

Find all angles a in radians that satisfy the equation Your answers should be formulas that look like angle k period where k 2 1 0 1 2 ranges over the integers 0 angle period and period is the smallest positive period that makes the formula work Note decimal answers are not allowed so for example if appears in your answer call it pi not 3 14159 The solutions of the equation are C or 2 sin x tan x sin x 0 A x

Find all solutions of the equation tan5 x 9 tan x 0 The answer is Ak where k is any integer the constant A

13 Simplify the expression algebraically sin 7x 7y sin 7x 7y O sin 7x cos 7y O sin 7x 7y O2sin 7x cos 7y O2 sin 7x O sin 7x 7y

7 Complete the table 0 sin 0 0 7 0 8 0 9 1 1 1

Find all solutions of the equation cos x sin x 2 cos x 0 The answer is A Bkn where k is any integer and 0 A T A 9 2 B

Find all solutions of the equation sec 4x 2 0 The answer is A and B where k is any integer and 0 A B 2 A B 9

Find the all solutions of this equation in the interval 0 2 X FI Give your answers in radians Do not use decimal approximations Use pi to represent Use commas to separate your answers tan x 10

If sin x A B cos 2x C cos 4x then A B C 4

If cos x 4 5 csc x 0 then sin 2x cos 2x tan 2x A G C

If cos x sin4 x A B cos 2x C cos 4x D cos 2x cos 4x then A B C D D G G

Use half angle formulas to fill in the blanks in the identity below sin 2x 4 cos x cos

Simplify the expression as much as possible sin 2x cos x help formulas

Use the formula for lowering the powers to simplify the expression a If cos 4x sin 4x cos f x then f x b If cos 4x sin 4x cos g x then g x Hint For part b use a b a b a 6

If tan 0 7 8 and cos 0 0 then sin 20 cos 20 tan 20 G 9 Fl

State the domain and range of each of the following functions Enter your answers as inequalities help inequalities Your domains should be inequalities in x and ranges in y As always type pi for T If you wish to enter type infinity a f x arccos x has Domain Range b g x arcsin x has Domain Range c h x arctan x has Domain Range

1 Korzystaj c 2 definicji granicy lim 2n 5 2 20 1 1 udownic

Find the exact value 8 2 cos 7 17 sin

Evaluate the following expressions Your answer must be an angle in radians and in the interval 2 2 Note that is already provided in the answer so you just have to write the appropriate multiple E g if the answer is 2 you should write 1 2 Do not use decimal numbers The answer should be a fraction or an integer a tan tan 7 6 b tan tan 57 4 c tan tan 7 4 G TT T

Evaluate the following expressions 2 sin sin 1 a b cos cos 0 1 c tan tan 1 D A CI

Find the domain and the range of g x sin 3x 1 A sas y Domain Range G F

Each expression simplifies to a constant a single trigonometric function or a power of a single trigonometric function Use fundamental identities to simplify each expression 1 sin x tan x cos x 2 sec x cos x 3 tan x cos x 4 sec x 1 5 tan x 2 sin x csc x CA 9 G

Evaluate the following expressions Your answer must be in radians written as multiple of 7 Note that is already provided in the answer so you just have to write the appropriate multiple E g if 2 is the answer you should write 1 2 Do not use decimals Your answer should be a fraction or an integer a tan 1 b tan 3 c tan 3

Evaluate the following expressions Your answer must be an angle T 2 0 in radians Give exact answers do not use decimal answers You can enter the number 7 as pi E g if the answer is 2 you could enter pi 2 or 1 2 pi sin 1 sin cos 1 os 1

oblem 3 Evaluate the following integral TT 3 6 cot x In sin x dx In 4 In 3 2 2 Problem 3 In 4 In 3 2 Just Save Problem 3 Enter your ansv as in these exa Submit Problem 3 for Grading Attempt 1 Attempt 2 At

Question Evaluate the indefinite integral given below Provide your answer below X5 x 2 dx

Evaluate the indefinite integral given below using the indicated substitution 3 4 42 x 3a 2 da U 3x x Provide your answer below

Fill in the blank to complete the trigonometric identity Simplify your answer complete COS

Use an identity to find the exact value of each expression Note You are not allowed to use decimals in your answer sin 2 T 3 3 COS os 7 6 tan TT TT F BI A

Solve the equations below exactly Give your answers in radians and find all possible values for t in the interval 0 t 2 If there is more than one answer enter your solutions in a comma separated list a sin t when t b cos t c tan t 3 2 1 3 when t when t A 94

Simplify the expression cos t 1 sin t sin t cos t 1 as much as possible help formulas

Simplify the expression as much as possible cos t 1 sin t N help formulas

Evaluate the indefinite integral given below using the indicated substitution fa Provide your answer below 17 8x dx u 17 8x

Use a calculator to approximate the value of the expression if possible Round your answer to the nearest cos 0 58

Calculate the binomial coefficient 16C15

Find the sum 5 i 0 41