Differentiation Questions and Answers

Evaluate the definite integral l ce GN x 1 2x 8 dx

The maximum number of turning points is n l The maximum number of zeros is n Example equation must have a minimum degree of 4 Tx Example Equation X x x 2 x 3 Maxima Minima Increasing Decreasing End Behavior x f x S x f x 4

4 Given the function below nd the f 4 D Increasing Ty f x 1 find x local max min absolute max min R Decreasing x intercept s

3 Find three mutually orthogonal unit vectors in R besides ti tj and k There are multiple ways to do this and an infinite number of answers For this probler component of a second vector v randomly and choose the first component of a third w chosen so that u v and w are mutually orthogonal Then unit vectors are found base Start with u 2 0 2 v x 1 1 and w 1 1 2 2 Type exact answers using radicals as needed The unit vector based on u is v 1 y z 0 The unit vector based on v is 1 1 1 3 3 3 Type exact answers using radicals as needed The unit vector based on w is Type exact answers using radicals as needed

a Determine the value of k for which the piecewise function g x 5x k Jutrascone audeliva silt to gribreterobnu viensrisiginos lins sybol word deuoted azu glinesoone alcornos in deney shiw is ni leyal betositzidqoz a to aleemuges lepimeentem zsilage bus supinist ensunsilsonog even remonte brir etisting exxingosen noitentie grignollado ni epimbost gnivioz molding aluam to vibiley bou sousailingiz odi znielqxs bas zbrstzishnu anolaudonoo asitizuj bus In lut swahl ennem stianos bus evitostio usols a ni zoitemsdem estroinummos anolzulonos inevoles x 1nftib mont egbolwomt stegetni of viilide sdi astmomsh golonims brus noite enabainia guiguslievs at domos2x 5 20 sa b Consider the graph of the piecewise function f x 3x 8 torto up 1 x 5 x 1 continuous x nos bas sabelwon x 5 estrenomad visitev a ni ainsmugte locitemedism silogs bus exam bris consuma bas amoting essingooon anoitaulia i Write down the coordinates of the y intercept vel mb brie aluasi to vtibiley bus sonsoilingi 30 392 ii Find the coordinates of the x intercepts immol bns noitsion coupinist toomos grien om sviests en morsilib moil allible bus gribnelasbar ogbalwonal dilanofionut 2 totaluolo lo sau insioilta esdem nousunie trattamericm acliqqs sandalla adi lo guibneleisbnu boog bns sabolwond boord s 20telanomo solsun shitvor ni pupindot gnizio maldon se and onituon gniotisqni einsmugis kas atxomo lo painsya ni esesong isoimmadiem to o vitezugovz 3 4

Convert the fraction to a decimal 4 5

Find the quotient Round to 3 decimals 40 44 10

Find the quotient Round to 3 decimal places 1 13 3 2

Find the quotient Round to 3 decimal places 9 5568 66

Round to the nearest hundredth 0 1744

What is the domain of the function y x O O 0 x 0 0 x 0 1 x 00 00 x 00

The radius of a circle with an area of 60 square centimeters is represented by the expression is another way of expressing the radius O2 15x 4 5x 2 15x SE 4 5x 60 X centimeters W

What is the following quotient 6 11 5 3 O O 17 8 57 30 3 2 55 33 8 30 3 2 55 33 2

If the range of f x mx and the range of g x m x are the same which statement is true about the value of Om can only equal 1 Om can be any positive real number m can be any negative real number m can be any real number

What is the range of the function y x 5 O y2 5 O y 0 Oy 5 O y 25

The orbital period P of a planet and the planet s distance from the sun a in astronomical units is related by th formula If Saturn s orbital period is 29 5 years what is its distance from the sun P a O 9 5 AU O 19 7 AU O 44 3 AU O 160 2 AU

Which function is undefined for x 0 O y x 2 y x 2 Oy x 2 Oy x 2 0 0

What is the following quotient 9 2 4 7 9 7 14 3 36 9 7 4 2 14 9 36 9 7 4 2 14 9 79

Differentiate the function f x sin x In 2x f x

Jse logarithmic differentiation to find the derivative of the functio x 3 y x 3 y

Differentiate the function G y G y In 4y 1 y 1

ifferentiate f and find the domain of f Enter the domain in interval notation f x In x 2x erivative omain

Differentiate the function 12 y In x y

38 The end of a 24 inch pendulum swings through an arc of 8 inches What is the measure in radians of the angle through which it swings Use the formula s re to find the correct answer A 192 radians B 3 radians C 3 3 radians D 3 radians

I have a vertical asymptote at x 0 with a domain of only positive numbers

10 Using the distance formula and the points 0 1 3 4 what is the second step in the solution A d 3 0 4 1 B d 3 0 4 1 C d 0 1 3 4 D d 0 1 3 4

For the vectors u 2 4 and v 3 2 calculate proj u and scal u proj u

9 Using these points 3 6 3 5 d A 11 OB 11 O C 1

4 Given A B C and D are collinear points in order B C AD10 BC 5 and AC 8 Find AB A 3 B 3 C 5 D

PART II Find the particular solutions of the given solutions satisfying the given conditions in each number 1 ex 4y c y ln 2 1 2 x y c y 1 1 3 4 5 cy x xy y 2 1 y tan x c y 0 0 2x cin x 212

Estimate the slope of the tangent line rate of change to f x x at x 1 by finding slopes of secant lines through 1 1 and each of the following points on the graph of f x x 10 9 8 7 6 5 a 2 4 10 9 8 7 4 3 9 secant slope msec b 1 5 2 25 10 9 8 secant slope msec

Solve for x 4 35 The exact solution using logarithms is a The approximate answer rounded to 4 decimal places is x

a Sketch the slope field for the differential equation b use the slope field to sketch the solution that passes through the given point and c discuss the graph of the solution as x 00 and x 00 Use a graphing utility to verify your results y y ay 0 4 5 2 1 2 1 2 Instructor 5 2 3

Define f x tan for x 1 Answer the questions using a plot if necessary Can f 1 be defined so that f is continuous at x 1 O No Yes How should f 1 be defined so that f is left continuous at x 1 Use symbolic notation and fractions where needed f 1

Identify the asymptotes domain and range of each function f x x 1 3 4 2 16 2 O f x 2 X

Yaster Car Sharing offers a membership plan with a 45 per month fee that includes 9 hours of driving each month and charges 9 for each additional hour Let F x be the cost for a month in which a member uses a car for hours Then F x is the piecewise function F x 45 for 0 x 9 F x mx b for x 9 for some scalars m and b Find b Round to the nearest whole number

1 point Apply the Laplace operator to the function h x y z ex sin 2y V2h

What position vector is equal to the vector from 0 4 7 to 4 2 5 The position vector is

Let Q t 2 Find a formula for the slope of the secant line over the interval 3 1 Express numbers in exact form Use symbolic notation and fractions where needed slope of the secant line Use the obtained formula for the slope of the secant line to estimate the slope of the tangent line at t 3 Use decimal notation Give your answer to one decimal place slope of the tangent line Find a formula for the slope of the secant line over the interval 4 1 Express numbers in exact form Use symbolic notation and fractions where needed slope of the secant line Use the obtained formula for the slope of the secant line to estimate the slope of the tangent line at t 4 Use decimal notation Give your answer to one decimal place

1 0 5 0 AI 7 4 180 23 150 4 135 210 120 225 240 0 1 kire 90 270 0 1 60 kim 45 300 30 f 330 315 ye opt 360 0 7 1 0 Use the unit circle to find two values of between 0 and 27 where cos 0 1 2 Separate the values with a comma Give the exact angle in radians no decimal values Ente for T

Determine lim g x for g as in the figure x 0 5 y 1 5 1 0 5 lim g x x 0 5 y g x X Give an exact answer Use symbolic notation and fractions where needed Enter DNE if the limit does no

The position of a particle at time t is s t 5t Compute the average velocity over the time interval 2 7 and estimate the instantaneous velocity at t 2 Give your answers as whole numbers average velocity over 2 7 instantaneous velocity

point se a triple integral to find the volume of the solid enclosed by the paraboloid x 4y 4z and the plane x 4

If there is more than one answer separate them with commas If the answer is an interval enter it in the form a b a b a b or a b Write infinity for and infinity for Click here for more help on entering intervals Let f x be the polynomial f x x 8 x 1 x6 5 What is the degree of the polynomial For what value s of x is the polynomial equal to zero On what interval s is the polynomial negative Not credit on this problem

x 6 Give an exact answer Use symbolic notation and fractions where needed lim f x x 6 1 lim x 6 f x lim x f x x 6

Let a b Let f be a bounded function on a b Let P P2 P3 be a sequence of partitions of a b such that lim P 0 n On each subinterval of each partition we pick x i 1 to be a point on the subinterval Which of the following must be true Select all answers that are correct There exists a partition P of a b such that lim Lp f Lp f n 0 n IF limf x Axi exists THEN f is integrable on a b i 1 Olim Lp f I f n n IF f is integrable on a b THEN limf x Axi exists i 1 n 00

1 point Consider the function f x y 8x x 6y y Find and classify all critical points of the function If there are more blanks than critical points leave the remaining entries blank fx fy fxx fxy fyy The critical point with the smallest x coordinate is Classification minimum local maximum saddle point cannot be determined The critical point with the next smallest x coordinate is Classification minimum local maximum saddle point cannot be determined The critical point with the next smallest x coordinate is Classification minimum local maximum saddle point cannot be determined local local local

5 4 3 2 5 4 3 2 1 y ON 1 1 234 3 1 2 3 4 5 4 15 Write an equation for the function graphed above

Let f x x If g x is the graph of f x shifted down 4 units write a formula for g g x

Give the slope and the y intercept of the line y 6 4x Slope 4 y intercept 6 Hint Is your intercept written as a POINT X