Calculus question and answers for January 22, 2024
- Q Find the limit If needed enter Inf for Inffor o or dne if the limit does not esist lim e 00 cos 4x
- Q Evaluate the following limits If needed enter Inf for Inf for or dne if the limit does not esist 5 A lim 2100 4 5 0 0
- Q Use linear approximation i e the tangent line to approximate 16 1 as follows Let f 2 2 The equation of the tangent line in slope intercept form to f...
- Q If z 8 and dy dt 5 when 2 and y Zensk dy dt 2 what is when 2 and y 2
- Q 2 Let y 4x 7x 4 Find the differential dy when 4 and dx 0 2 Find the differential dy when x 4 and da Sam 0 4
- Q find x cos x 8x sin x 4x Find 2 4x tan x 4x 2 tan x 2 sec x f x 42 ta sec
- Q Indicate the answer choice that best completes the statement or answers the question Which function is an odd function Oa f x 2x b f x x 4 Oc f...
- Q 5 The graph of g is shown to the right Which of the following statements are true of g at x d 1 g is continuous 11 g is differentiable...
- Q f x x Let x be any arbitrary element of R then Right hand limit at x x lim f x lim f x h X X Institute of Lifelong...
- Q AP Multiple Choice Problems 5 Derivatives and Limits No Calculator Be sure to show some work or give an explanation A 1 only B 2 only C 4 only D...
- Q 1 Suppose that the height of a skydiver t seconds after jumping from an airplane is given by s t 4500 20t 16t2 feet neglecting air resistance The skydiver pulls...
- Q II I Discontinuity of the First Kind from the Left at x The function f X R is said to have a discontinuity of first kind from the left at...
- Q Now let a be any arbitrary element of R then there arise two cases Case I If a 0 then and 1 lim f x lim x sin X NI...
- Q Find y by implicit differentiation Match the equations defining y implicitly with the letters labeling the expressions for y 1 5x cos y 4 cos 2y 3 sin y 2...
- Q Sammen A particle is moving along the curve y 3 4z 1 As the particle passes through the point 2 9 its coordinate increases at a rate of units per...
- Q The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute How fast is the volume changing in cubic centimeters per minute when the radius...
- Q Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second How fast is the radius increasing after 2 minutes Note The volume of a...
- Q Find the slope of the tangent line to the curve at the point 77 7 2 4 sin z 3 cos y 2 sin r cos y z 7
- Q 3 Let y 28 Find y x at the point 3 1 3 3
- Q Find dy de by implicit differentation dy da 4 2x sin xy
- Q The linear approximation at z 0 to f x where B 1 5 I is L x A Br
- Q Suppose xy 4 and dt 11 dy dt 1 Find dx dt when a 3
- Q dy If y xy 3x 7 and dr 2 when a 3 and y Genti 1 what is when 3 and y 1
- Q If z y 8 and dy WI dr dt 5 when t 2 and y 2 what is dy when 2 and y 2
- Q If 5x 2x xy 4 and y 4 21 find y 4 by implicit differentiation
- Q For the equation given below evaluate y at the point 1 2 y at 1 2 5x y 2y 97
- Q Let f x 2x 3 2 2 x 3 4 2x 3 2x 3 5
- Q da 9 sect tan dt Now substitute and simplify to get a trig integral in terms of t The trig integral should no longer involve a square root 81 da...
- Q 1 Assume that f x is a function on the interval 0 1 that has a Fourier sine series on 0 given by 00 give the value of ba 1...
- Q The bar graph below shows that as costs changed over the decades a group of people devoted less of their budget to groceries Percentage of Total Spending on Food Percent...
- Q the function defined above then lim f x is B 0 f x x 1 2 for a for a 1 1
- Q Part 1 The Partial Fraction Setup Since the degree of the numerator is less than the degree of the denominator begin by using polynomial long division to reduce the degree...
- Q The goal of this problem is to evaluate 1 Because the sine term has an odd power the first step is to rewrite sin x sin x sin x sin...
- Q da sin z 12 COS 12 Now substitute and simplify to get a trig integral in terms of t The trig integral should no longer involve a square root Tz...
- Q Part 1 The Partial Fraction Setup 4x 3 and find the values of the 3x 5 x 3 Perform the partial fraction decomposition of coefficients Give the coefficients as exact...
- Q The goal of this problem is to evaluate Part 1 The Partial Fraction Setup 82 16 x 8x Perform the partial fraction decomposition of 8x 16 x28x dx using partial...
- Q B 3 tan t da 3 sec tdt Now substitute and simplify to get a trig integral in terms of t The trig integral should no longer involve a square...
- Q For each of the following integrals give an appropriate trigonometric substitution of the form f t to simplify the integral x 9 x dx a 2 9 x 49 dx...
- Q The goal of this problem is to evaluate 121 2 de using trig substitution Click on Part 1 to open the section Enter your answers for the three steps in...
- Q 2 The function G x 0 01x x 66 models the wage gap as a percent x years after 1980 in Country A The graph of function G is shown...
- Q Plot the ordered pair 7 6 on the rectangular coordinate plane Plot 7 6 a 2 2 10 B 6 10 8 84 2 Ay 4 6 8
- Q The goal of this problem is to evaluate J cos 2x cos x dx First convert this to a new integral with cos 2x cos x rewritten as the sum...
- Q 2 Evaluate each limit Use algebraic methods if possible If not use graphs or tables x 7x 12 x 9 2K 4K a limx 31 X 8 b limx 8...
- Q 3 a What does the limit lim 0 f h 4 f 4 h 8 indicate about the function f x x
- Q NA Determine if the function is even odd or neither Even O Odd ONeither
- Q a Are the events A and C independent Justify your answer b Are the events A and D independent Justify your answer c Compute 1 P AB and P AB...
- Q Which function is always increasing O x 1 O x 1 O x 2x 1 Ox 2x
- Q Which inequality has a solution set of 5 00 0 1 4 0 1 4 0 1 4 02 124
- Q 2 4 3 1 5 2 O 3 1 5 0 2 O 2 3 1 5 Find the solutions to the function 2 O 1 5 1 3 5...
- Q 2 O 2 2 O 1 3 O 2 2 0 2 T Where is f x increasing Give your answer in interval notation
- Q Which function has an x intercept of 12 and a y intercept of 3 Oy 4x 3 Oy 3x 12 O y 12x 3 Oy z 3
- Q Which function has a domain of 0 2 U 2 00 O 3x x 2 20 x 2 O x 2 8
- Q Given f x 3x 4 and g x 5x 2 find 2f 4 O 6x 8 O 16 O 32 O 2 3x 4
- Q Given f x 3x 4 and g x 5x 2 find 3f x 2g x O 25 9x 12 19x 16 A
- Q The goal of this problem is to evaluate sin cos da using substitution 1 Because the cosine term has an odd power the first step is to rewrite cos5 x...
- Q 1 27 100 1 000 1 4 81 x 33 0 25 2 4 36 5 7x 6 30
- Q The goal of this problem is to evaluate cos 2x cos x dx First convert this to a new integral with cos 2x cos x rewritten as the sum of...
- Q Find a if a 2log 4 log 5 log 10 log a b log 30 log 52 log c c log 8 log x log x d log x 2...
- Q 2 31 3 9 x 34 5x 1 0 04 2 4 37 e x 2 et 1
- Q 1 36 32 0 01 2 100 5 29 62 x 3 35 4 7 15 38 3x 2 36
- Q 5 5 x 9 8 b 5 3 2 1 11 5x 40 4 14 2x 3 17 z 81
- Q 3 x 4 X3 6 b 8 9 2y 12 1 12 5x 7 22 7 81 215 3a
- Q 13 14 4b 2
- Q 4 15 x y6 x y5
- Q What is the maximum value of z 3x 4y for the region given by the system I 0 y20 x y 11 3x 2y 30 Choose the correct answer for...
- Q Solve for a in the given matrix equation 1 2 3 det 1 x 1 26 2 3 4 Choose the correct answer a x 2 Ob z O c...
- Q I Q 1 3 1 Continuity from the Right at a Point A function f X R is said to be right continuous or continuous form the right at a...
- Q 5 1 Types of Discontinuity Let f be a function defined as f X R and let xeX and let left hand limit right hand limit limit of the function...
- Q 1 Place the phases of the business cycle in order Recession Trough Peak Expansion How long do each business cycle last
- Q Let V 1 2 3 n Let X i j i je V and are relatively prime The resulting graph V X is denoted by G Draw G4 and G5...
- Q So the appropriate domain for this situation is all non negative real numbers or in interval notation 0 00 b The range of a function refers to the set of...
- Q What are the extrema of f x 2x 2 4x 2 What are the domain and range of the function
- Q 6 The battery charge of a cell phone is tracked with a function over the course of one day Graph a possible function below that correctly represents the domain and...
- Q 8 A wedding caterer charges a 200 service fee and 24 per plate cost of food for one guest Johanna has gotten RSVPs from 72 guests but is still waiting...
- Q 9 Which of the following functions has a domain given by x Rx 4 A f x x 4 B g x x 16 C h x 9 x D...
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