13) In Problems 13 through 20 given f(x) and g(x) are Continuous and DifferentiableEVERYWHERE withX =f(x)g (x)f' (x)8' (x)12- 171D 163-3-2PropertyFind lim [3 f(x) – 4 g(x/3)] =.X→3A) 1В) 3C) -11D) 17And14) Find lim [g(x-2)/f(x-4)]=_A) 1/7B) 1/3C) 3/5D) 7/315) Find lim g[f(x-1)]=__x→2A) 3B) 1C) 7D) 5

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Answered: 13) In Problems 13 through 20 given…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Show that the solution of initial value problem: d^2x/dt^2 + w^2x = F0cosAt, x(0)=0, x'(0)=0 is x(t)= F0(cosAt-coswt)/(w^2-A^2). b) Evaluate lim,y>w F0(cosAt-coswt)/(w^2-A^2).
13. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]
1. Find the absolute maximum and minimum values of f(x)=10x(2-lnx) on [1,e^2] 2. Find the limil. Uisng L'Hopital's Rule : lim x arrow 0 sin^2(3x)/4x
5. Consider the function f(x) = |x| + 2 at x = 0. Provide a table of inputs and outputs that demonstrate the limitdefinition of the derivative, numerically
a) Evaluate in terms of Gamma function ∫e^(−y^2) y^13 dy limit 0 to ∞ b) Find ∫f(x) dx limit: 1 to 38 if ∫f(x) dx=−17 limit -19 to 1 and ∫f(x) dx=10. limit : -19 to 38
2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) = 2(1-x)/1+x^2 and f"(x)= 4x(x^2-3)/ (1+x^2)^2 Further, assume that it is known that f has a horizontal asymptote at y = 0. and a. Determine all critical points of f.
2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
Sketch the graph of a continuous function ƒ on [0, 4] satisfyingthe given propertie. ƒ'(x) = 0 for x = 1, 2, and 3; ƒ has an absolute minimum atx = 1; ƒ has no local extremum at x = 2; and ƒ has an absolutemaximum at x = 3.
The limit of (xy-2y) / (x2+y2-4x+4) as (x,y) approaches (2,0) is solved and found out that it does not exist. Can we make this continuous by defining f(2,0) = k for some real value k? If yes, what could this value be? If no, why not?
Problem 9 The volume of the solid obtained by rotating the region bounded by x=(9y^2), y=1, x=0 about the y-axis can be computed using the method of washers or disks via an integral V=∫________________dy (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dx (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________ In either case, the volume is V=______________ cubic units
Sketch the graph of a continuous function ƒ on [0, 4] satisfyingthe given propertie. ƒ'(x) = 0 for x = 1 and 2; ƒ has an absolute maximum at x = 4;ƒ has an absolute minimum at x = 0; and ƒ has a local minimum at x = 2.
Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=

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