Calculus Questions

0 24 Shiple points to be left endpoints Round your answer to six decimal places 2006343 What does the Riemann sum represent The Riemann sum represents the net area of the rectangles with respect to the Illustrate with a diagram 5x 00 24 77 8 Select y axis x axis D origin KIT 4 500 3 KIN 00 24 tat t

a On what interval s is increasing Enter your answer using interval notation 1 6 U 8 00 On what interval s is f decreasing Enter your answer using interval notation 0 1 U 6 8 b At what value s of x does f have a local maximum Enter your answers as a comma separated list x 6 At what value s of x does f have a local minimum Enter your answers as a comma separated list x 1 8 c On what interval s is f concave upward Enter your answer using interval notation

O IN Sketch the graph of a function that is continuous on 1 51 and has the given properties absolute maximum at 2 absolute minimum at 5 4 is a critical number but there is no local maximum or minimum there 6 Kinh 1 4 2 6 6 1 2 3 4 5 2 3 ASK YOUR TEA

00 DETAILS SCALCET9 4 9 057 The graph of a function is shown Which graph is an antiderivative of 3 0 2 0 1 0 1 0 2 0 5 1 0 1 5 2 0 b 2 5 a

Three coins are tossed Consider the odds against getting three heads How many different outcomes are possible outcomes How many of the possible outcomes are three heads outcomes How many of the possible outcomes are not three heads outcomes What are the odds against getting three heads

2 O No 4 6 Are the secant line and the tangent line parallel Yes Show My Work Required Wha 8 or reasoning did you use Your work counts towards your score

Consider flipping a coin five times How many outcomes are possible 4 Let F obtain at least one head in five flips of a coin What does the event F represent P F obtain Select heads in five flips of a coin Find P F Find P F the probability of obtaining at least one head in five flips of a coin Enter the probability as a fraction

Consider a bowl containing 120 marbles 20 green 18 blue 20 gray 7 orange 4 yellow 21 cat eyes and 30 multicolored Suppose each marble has an equal chance of being picked from the Find the following probabilities Round your answers to three decimal places a P gray b P cat eye c P multicolored

For the spinner below assume that the pointer can never lie on a border line Find the following probabilities Enter the probabilities as tractions a P D b P E c P F Need Help Read It Additional Materials F Tech Guide Excel E

The graph of the polynomial f x is given below If f x has degree 4 find the factored equation for f x Provide your answer below f x 3 2 1 2 31 2 w 3

Player Babe Ruth Willie Mays Ty Cobb Walter Johnson Hank Aaron Is the rank a function of the player name Is the player name a function of the rank Select the correct answer below Rank 1 2 3 4 5 Rank is a function of player name but player name is NOT a function of rank Rank is NOT a function of player name but player name is a function of rank Rank is NOT a function of player name AND player name is NOT a function of rank Rank is a function of player name AND player name is a function of rank

Which of the following are binomials Select all correct answers Select all that apply 3x y 3x 3x y 3x 3x y z 2x yz 3xy 2x y z 3xyz

16 8 points Use the method of Lagrange multipliers to find the points on the surfa r yz 4 closest to the origin

Identify the expression below as a monomial binomial or trinomial 6x 8 Select the correct answer below Monomial Binomial Trinomial

Which of the following are trinomials Select all correct answers Select all that apply 3pq 2p 2p qr 3p q 3pqr 3p 2p q C 2 S 2pg 3pgr

Find the leading coefficient of the following polynomial 5 x 3x x4

Find the degree of the following polynomial 5 x 3x x

Find the leading coefficient of the following polynomial 5x 7x 6

Find the degree of the following polynomial 5x 7x 6

Question 1 A car moved distance S meters in a time t seconds according to the formula S 3t 2t 4t 1 Determine 1 1 velocity at i t 0 ii t 1 5s 1 2 Acceleration at i t 0 ii t 1 5s Question 2 Let f x x 2x 1 2 1 Find the equation of the tangent at x 1 2 2 Determine the equation of the normal to the tangent line at x 1 Question 3 If f x 3 1 Determine the equation of the tangent at x 1 3 2 Determine the equation of the normal to the tangent line at x 1 Question 4 Determine the derivative of the following functions with respect to the independent variables 4 1 yxsinx cos 2x sin 4x 4 2 y Question 5 Use logarithm differentiation techniques to determine the y of the following functions 5 1 y 5 2 Inx cos3x x sin3x e t sin 2t 5t Question 6 Determine the derivatives of the following inverse trigonometry functions tan x 6 1 f x 6 2 h t tcos 1 et 5 3 3 3 4 4 5 6

20 points Find the matrix exponential e for the given system 21 t 0 2 5 3 t 00 2 Then use it to find a solution satisfying the initial condition 7 0

Test whether the Gauss Seidel iteration converges for the system 0237 the 2x x x3 4 X 2x x3 4 x x 2x3 4 Use a suitable norm in your computations and justify the choice

Write the following numbers in the polar form re 0 0 2 1 8 a T b 7 7i T c 3 3i T 0 0 0

Rewrite the complex number 6e4i in a bi form

Find all the real zeros of the following polynomial Provide your answer below f x x6 1000x

Let f R R be a function satisfying 2 x f 2 x and 20 x f x x R On the basis of above information answer the following question 15 50 Read Less

Find the zeroes of the following polynomial f x x 4x Provide your answer below 21x List the zeroes separated by commas For example if you found that the zeroes were x 1 x 2 and x 3 you wou enter 1 2 3

An engineer is building experimental dome shaped living quarters 24 m high and modeled by the function z 24 2x 3y She wants to bolt a flat solar panel to the dome at the point 2 2 4 Find the vector of the direction in which the engineer should drill Give your answer using component form or standard basis vectors Express numbers in exact form Use symbolic notation and fractions where needed

Find the zeros of the following polynomial f x x 49x List the zeros separated by commas For example if you found that the zeros were x 1 x 2 and x 3 you enter 1 2 3 Provide your answer below

Select the correct answer below 7654321 6 5 4 7 6 5 4 3 2 11 2 EL 2 127 4567 4 5 6 7 T 2 3 4 5 6 7 x 4 with multiplicity 1 x 4 with multiplicity 1 and x 1 with multiplicity 2 x 4 with multiplicity 1 x 4 with multiplicity 2 and x 1 with multiplicity 1 x 4 with multiplicity 2 x 4 with multiplicity 1 and x 1 with multiplicity 1 Ox 4 with multiplicity 1 x 4 with multiplicity 2 and x 1 with multiplicity 1

Given the polynomial f x x 3x what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 1 and a Enter an integer as your answer For example if you found a 8 you would enter 8 Provide your answer below

Based on the degree of the polynomial f x given below what is the maximum number of turning points the graph of f x can have f x x 8 x 3 x 5

Given the following table of values of the polynomial f x what is the minimum number of zeros of f x that are guaranteed to exist by the Intermediate Value Theorem Select the correct answer below 0 1 2 3 X 1 2 3 4 5 6 f x 3 8 5 10 32

Given the graph of y f x shown as a red dashed curve drag the movable blue point to obtain the graph of y f x 4 2 Provide your answer below 10 5 f x 10 5 5 5 10

y f x 4 2 Provide your answer below 10 5 10 5 0 5 f x 5 10

Find the inverse of matrix A defined by Provide your answer below 2 4 1 Use the matrix tool to enter your answer Use fractions when necessary

Which of the following matrices are invertible Select all correct answers Select all that apply 3 2 4 5 2

Solve the following system of equations by using the inverse of a matrix 4x 6y 6z 54 9x Z 3 8x 2y 3z 21 Give your answer as an ordered triple x y z Use fractions when necessary

Is the following matrix invertible Select the correct answer below Yes the matrix is invertible No the matrix is not invertible 435 3 3 2 4 4 5

3 3 47 3 3 find det A Given the matrix A 4 4 3 1 2

Given the following system of equations use the inverse of a matrix to solve for the values of x and y Give your answer as an ordered pair If no solution exists enter 2x 4y 4 x y 1

Determine if matrix A given below is invertible Select the correct answer below Matrix A is invertible Matrix A is not invertible A 6 3 6 5 1 1 2 1 5

a Find the largest possible open interval s on which f is increasing and the largest possible open interval s on which f is decreasing Select the correct choice below and if necessary fill in the answer box es within your choice 13 A The function is increasing on the open interval s 8 12 and decreasing on the open interval s 7 8 Simplify your answer Type your answer in interval notation Use a comma to separate answers as needed B The function is decreasing on the open interval s The function is never increasing Simplify your answer Type your answer in interval OC The function is increasing on the open interval s The function is never decreasing notation Use a comma to separate answers as needed Simplify your answer Type your answer in interval notation Use a comma to separate answers as needed OD The function is never increasing nor decreasing A The critical point s are located at x 8 10 Use a comma to separate answers as needed B There are no critical points b Find the critical points of f Which critical points correspond to local maxima Local minima Neither Find the critical points of f Select the correct choice below and if necessary fill in the answer box within your choice Which critical points correspond to local maxima Select the correct choice below and if necessary fill in the answer box es within your choice A The critical point s x correspond s to local maxima Use a comma to separate answers as needed B There are no critical points that correspond to local maxima

Evaluate the integral using only methods taught in class and simplify your answer Do not skip steps Use either the Finger Method or the Plug and Chug Method to find coefficients when it is possible to do so if you don t no credit will be given x x 1 x 1 x 2 dx

8 Let E be the solid region above the cone z x y and inside the sphere x y z 1 If the density is given by 8 x y z a Set up an expression in Rectangular Coordinates of the mass b Using Spherical Coordinates find the mass

4n Determine whether m is convergent or divergent Use only methods taught in this 5n 1 class 4n tor divergent Ilse only methods taught in this

Given the polar equation r 4sin 30 a Sketch the polar graph by first graphing the cartesian graph Show the exact correspondence between sections of the two graphs I e do it exactly the way that was shown in lecture

Find fis x dx by using the formula for the area of a triangle 8 8 x dx Simplify your answer

Choose the correct answer below A A level curve is the intersection of the surface with a plane parallel to the xy plane B A level curve is a plot that is made of various traces graphed on one set of axes C A level curve is the intersection of the surface with the yz plane or the xz plane OD A level curve is the trace that results from a surface being cut by a slanted plane

Use the Shell Method to find the volume V of the solid obtained by rotating the region bounded by the following curves about the x axis Draw the 2D region the resulting 3D volume of revolution a typical shell state dV get everything in terms of x or y queen variable and finally integrate to find V Use only methods taught in this class x 3 y 6 x 19