# Calculus Questions

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Calculus
Application of derivatives
A particle has a velocity modeled by v t 6 2 ln t 8 measured in cm s over the interval 1 t 6 What is the distance traveled from t 1 to t 6 You may either enter an exact answer or round your answer to the nearest tenth of a centimeter Provide your answer below
Calculus
Differentiation
4 3 x2 Find the derivative
Calculus
Differential equations
Suppose the rate of growth of bacteria in a Petri dish is given by q t 6 where t is given in hours and q t is given in thousands of bacteria per hour If a culture starts with 7000 bacteria find a function Q t that gives the number of bacteria in the Petri dish at any time t How many bacteria are in the dish after 4 hours You should round your answer to the nearest whole number Do not include any commas in your final answer if applicable Provide your answer below bacteria
Calculus
Application of derivatives
Evaluate the indefinite integral given below 6x x 4x x x2 dx
Calculus
Indefinite Integration
Question Find the price demand equation for a particular brand of toothpaste at a supermarket chain when the demand is 36 tubes per week at 1 65 per tube given that the marginal price demand function p x for x number of tubes per week is given as p x 0 02e 0 04x If the supermarket chain sells 70 tubes per week what price should be set Round to the nearest cent Provide your answer below
Calculus
Vector Calculus
Use substitution to evaluate the indefinite integral Provide your answer below f In 2x dx 5x In 2x 5x dx
Calculus
Indefinite Integration
Evaluate the indefinite integral given below e 20 Provide your answer below S e 2 csc 2x 2 csc 2x cot 2x csc 2x dx wwwww 2 csc 2x cot 2x csc 2x dx
Calculus
Application of derivatives
A triangle has an area of 7 in and two of the sides of the triangle have lengths 5 in and 4 in Find the angle included by these two sides 45 573 O 0 795 44 427 no correct answer
Calculus
Application of derivatives
Find a function that models the simple harmonic motion having the given properties Assume that the displacement is zero at time t amplitude 2 3 m frequency 0 5 Hz O f t 2 3 sin t O f t 2 3 sin 2t O f t 2 3 sin 2 t O f t 2 3 sin at O f t 2 3 sin 0 5 t
Calculus
Application of derivatives
Graph g x x on the Cartesian plane to the right The domain of g x is The range of g x is If any of the above do not exist leave the answer box blank 654 ch 2 10 9 8 7 6 5 4 3 2 21 6 7 8 9 10
Calculus
Application of derivatives
Find the terminal point P x y on the unit circle determined by t O 0 87 0 50 O 0 87 0 50 O 0 87 0 50 O 0 99 0 64 5TC 6 Round each value to the nearest hundred
Calculus
Vector Calculus
Find the equivalent expression 1 sin x 1 sin x 1 sin x 1 sin x O 4 tan x sec x O 4 cot x csc x O4 tan x sec x O 4 cot x csc x O 4 cot x sec x
Calculus
Limits & Continuity
Use the Law of Sines to solve for all possible triangles that satisfy b 23 c 35 LB 25 conditions O ZA 119 LC 39 a 51 O ZA O ZA O ZA 117 LC 114 LC 1150 LC 40 a 55 42 a 47 40 a 49
Calculus
Vector Calculus
Evaluate the indefinite integral given below Provide your answer below 20 5 dx 2e 6 x4 X5 31 dx
Calculus
Application of derivatives
Use the Law of Sines to find x Let c 21 LA 58 25 24 O 46 23 A C C X 70 B
Calculus
Application of derivatives
What is the side labeled x equal to if y 22 22 O 11 O 44 Y 30 X
Calculus
Application of derivatives
Find the reference angle for the angle measuring O O 4 T 11 4T 15 11 4 4 T 11 15T 11
Calculus
Vector Calculus
The measure of the angle 330 in standard position is given Find two positive angles and two negative angles that are coterminal with the given angle 670 1 060 70 345 690 1 050 30 390 O 710 1 020 50 360 426 786 294 654
Calculus
Definite Integrals
Evaluate the definite integral below Enter an exact answer Provide your answer below S 1 3x 4x 4 dx L 3x 3 4x 4 dx
Calculus
Definite Integrals
If you were to use a substitution of u sin x to evaluate the definite integral below what would the new limits of integration be Enter an exact answer Provide your answer below The new lower bound is 1 6 sin x cos x dx and the new upper bound is
Calculus
Limits & Continuity
20 20144338 6d168319ac2e5dbf490 c0867dd8733e6 Question 42 11 09 Watch Video Graph the function f x 3 1 on the axes below You must plot the asymptote and any two points with integer coordinates Asymptote Horizontal Show Examples
Calculus
Definite Integrals
Use substitution to evaluate the definite integral given below Enter an exact answer Provide your answer below M 2 x sin 3x cos 3x dx x sin 3x cos 3x dx
Calculus
Indefinite Integration
Evaluate the indefinite integral given below S sin x 3 sin x sin x 4 sin x cos x dx Provide your answer below f sin x 3 sin x sin x 4 sin x cos x dx 4
Calculus
Definite Integrals
1 06011 5 5 8 3 The answer above is NOT correct Find the exact length of the curve given by x 2t y 1 3 0 t 1 incorr
Calculus
Definite Integrals
A mining company owns two mines These mines produce an ore that can be graded into two classes regular grade and low grade The company must produce at least 420 tons of regular grade and 540 tons of low grade ore per week The first mine produces 6 tons of regular grade and 18 tons of low grade ore per hour The second mine produces 18 tons of regular grade and 9 tons of low grade ore per hour The operating cost of the first mine is 20 000 per hour and the operating cost of the second mine is 9500 per hour The first mine can be operated no more than 37 hours a week and the second mine can be operated no more than 28 hours a week How many hours per week should each mine be operated to minimize the cost Note that the ALEKS graphing calculator can be used to make computations easier hour s Second mine hour s First mine
Calculus
Vector Calculus
Find the missing side lengths Leave your answers as radicals in simplest form 25 26 30 7 3 A x 7 3 y 14 B x 14 y 7 C x 7 2 y 7 D x 7 2 y 7 3 A 60 5 3 y A x 10 y 5 B x 10 3 y 5 5 3 C x 10 3 y 3 5 3 D x 10 y 3
Calculus
Differentiation
27 3 J 2 30 A m 3 n B m 2 5 n 3 C m n 2 3 D m 3 n 2 28 4 5 3 45 y 5 3 3 S 6 A x B x C 5 6 D x S 6 6 5 3 y 39 6 5 6 3 y y 5 y 5
Calculus
Limits & Continuity
Graph each function Lable all asymptotes lable any x y intercepts 4 x 2 22 f x A D 21 f x A B C 2 2 H B C D 3 x 2 The 4 M
Calculus
Vector Calculus
Find the value of each trigonometric ratio 29 tan X 20 30 50 40 355554 Z 30 tan C B 12 U 35 20 37
Calculus
Application of derivatives
D C 23 S x 1 A B AH 24 S x 2 1 A B 6 D 2
Calculus
Limits & Continuity
14 f x x 5 A S x x 3 B x x 5 C x 4x 4 D S x 1 x 15 g x 3 x A g x 5 Sx 25 2 3 B g x x 2 8 9 C g x x 4 2 D g x 2x 6 8
Calculus
Application of derivatives
Divide Write your answer in fraction form 16 x 6x 10x 10x 16 x 1 11 A x 5x 5x 5 x 1 B r 5x2 5x 5 6 C r 5x2 5x 5 D x 3x 4x 6 x 1 6 x 1 6 x 1 17 4x 25x 28x 6 x 5 A 4x 5x 3 B 4x 5x 3 C 4x 5x 3 D 4x 5x 3 9 x 5 2 x 5 2 x 5 9 x 5
Calculus
Vector Calculus
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
Calculus
Limits & Continuity
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
Calculus
Definite Integrals
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
Calculus
Limits & Continuity
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
Calculus
Application of derivatives
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
Calculus
Application of derivatives
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
Calculus
Application of derivatives
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
Calculus
Differentiation
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
Calculus
Application of derivatives
Do 3 Determine the number of grams in the following A 15 85 moles of Helium 63 45gte 142atte 1 th
Calculus
Application of derivatives
B 71 60 g Si 2 549 mores Si 28 085951 71 600 Spo mole si
Calculus
Indefinite Integration
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
Calculus
Application of derivatives
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
Calculus
Application of derivatives
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
Calculus
Application of derivatives
21 Find the exact values of the three trigonometric functions sine cosine tangent of the real number t a b a D 5 13
Calculus
Application of derivatives
1 point Find the exact length of the curve given by 1 t 3 Length X 2t y 0 t 1
Calculus
Application of derivatives
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
Calculus
Application of derivatives
Find all solutions of the equation tan5 x 9 tan x 0 The answer is Ak where k is any integer the constant A
Calculus
Application of derivatives
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