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Q: [sin (zx), 0<x<1 lax+b, 1<x<4 17. Let f (x)= { f(x) is Find the values of a and b such that…

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Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x&lt;πmx+b,      x≥π Since the function fx is continuous…

Q: Let 1(2) = sin(rz) (1- h)? + k :>: (a) Find values of h and k so that ƒ is a differentiable…

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Q: What is the maximum value of y = cos x. For -5 < x <? 1 2 O 1/2

A: Topic = Derivative

Q: [Q2] Find a root of the function using the secant method with initial guesses of x-1 2 and xo 2.6.…

A: Introduction: A transcendental equation can be solved numerically. The base of solving a…

Q: - 1 X If lim ([sin ¹x] + [2²sin ¹' (2x)] + [3³ sin-¹ (30)] x →0 X X + [x²³sin-¹ (x2x)]) + ... +…

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Q: 4 35₂ In evaluating 2 dx X√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at x= 2.9.

Q: 1. Find the value/s of b such that the function f is continuous everywhere. x3 + 2, x 0

A: In the question we have to find value of b.

Q: 5) Find all possible oblique asymptotes for following functions: y = Vx² + 1 2x/2+2x-3 y = Vx+1 y =…

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Q: a. Let ƒ(x) be a function satisfying 0 ƒ(x) 0 … x2 for -1 … x … 1.Show that ƒ is differentiable at x…

A: The differentiability of the function can be determined with the help of the left-hand derivative…

Q: * 3x ], the x-coordinates of the points on the graph of the function f(x) = 1 + cos x where the…

A: For horizontal  tangent dy/dx=0

Q: 1 Find Maclaurin polynomial P, to f (x )= : 1 1 cosx sin Ax 1-x 1+x

A: According to bartleby guideliness we can answer only the first three subparts of a question. kindly…

Q: 3sin-1x, if -1< x< 0 f(x) = x2+ Tt if x20 x+cosx'

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Q: #2. Verify Clairaut's Theorem for the given function f (s, t)= In (st)-s* sin (6t) +st.

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Q: (b)Consider the piecewise function S (1+ æ)ª – 1, if x>0 = (x) 6 I sin (4x), if æ < 0. Discover…

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Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, s" (÷) = -1, and g(r) = log…

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Q: Which of the following is true about the graph of f(x)-2 sin3 (x) + 3 sin(x) + 4 on the interval [0,…

A: Definition used:An inflection point is a point on a curve at which the sign of the curvature or…

Q: Give an example of a (discontinuous) function that does not satisfy the conclusion of the IVT on…

A: Given: f(x)=sin1x    x≠00            x=0

Q: We have f(x): f(x) = {sin2x 0 >ܝ TT 2 <x< O. W. a)find the coefficients and show that Vx € [-^,^]:…

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Q: Let f(x): e² sin³ (4) x6 sec(x − 2) a. Solve for f'(x) without using quotient rule or product rule.…

A: As per the question we are given the function f(x) and we have to find its derivative f'(x)  without…

Q: b. b-a Use the equation fte)dx = lim ** ) to evaluate the following definite integral. n-0k=1 2 |(2x…

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Q: -x² +1 1- sin? x if x20 if x <0 Let f(x) be defined as f(x)= • Is f(x) differentiable at x = 0? • Is…

A: Answer and explanation is given below..

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. Prove that h' is not differentiable at x = 0. .

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Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

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Q: At what x values in the interval [0, 27] does the function f(x) = sin² (x) – sin(x) have a %3|…

A: Given that: f(x)=sin2x-sinx

Q: 3. Determine any points of relative extrema of g(r) = 2 sin(x)- -r on 0, 271. %3D

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Q: sin 7Z „Find the residue of f (z)at z = 4 (z – 4)? Let f (z) =

A: Note:

Q: cos x+sin x-e 2 cos x-2 cosh y If f (z) = u + iv is an analytic function of z and u-v = prove that…

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Q: Suppose f and f' are differentiable functions of r. Given f' (=) = 0, f" (4) = -1, and g(x) = log…

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Q: 3. (a) Let f be differentiable on an open interval I and suppose f"(x) = 0 for every x in 1. Show…

A: Let f be a differentiable on an open interval I i.e. (a,b), Suppose that f'(x)=0 for every x in…

Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…

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Q: 116. a. Show that if ƒ is odd on [-a, a], then f(x) dx = 0. -a b. Test the result in part (a) with…

A: a.  Now put

Q: 1+ x² -L „tanx - for all x €[0,1/2], then f'(x) equals 1+ ex * If f(x) = sec2x A 1+ etanx sec³x B 1+…

A: Given an integral. We need to find f'(x).

Q: 5. Find the exact absolute maximum and absolute minimum values for 2 f(x) = cos(x) + sin´(x) on the…

A: We have to be find

Q: Consider the function f(x) over the interval 0, 1. Does the extreme value theorem guarantee the…

A: Given function is f(x)=1sin πx4 over the interval 0, 1 and  q(x)=4x+32x2-1 Extreme value theorem: If…

Q: y for the function f(x)= cos [x*sin (x²+1)] =, CoS 1/2 %3D ..…

A: The given function is fx=cos3x3sin12x2+1. Obtain the derivative as follows.

Q: sin TZ Let f (z) = Find the (z – 10)² residue of f (2)at z = 10. -

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Q: dx For = In[F(x)]+C•What is f(/3) if C = 0? (x+x³) (x Tan-lx+ 1) -1 + - - 3. -1 + - + S-is-isS

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Q: 1. Consider the function f defined on [0, ∞), 1 f(x) = sin- x + 0 x = 0

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Q: (1) Locate the absolute extrema of the function on the closed interval. (a) y=4 sin x, [0,2n] (b)…

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Q: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) >= 0 for x element…

A: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) &gt;= 0 for x element…

Q: 1. Find the value/s of b such that the function ƒ is continuous everywhere. f(x) = {6x – sin bx 0 <x

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Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: Limit as t goes to 0 of    (t^3+3t) / sin (5t)

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Q: 5 find aroot of the eqution f(x)=x²-4 Sinx = 0 using the 2 Newton-Raphson, Xo = 3,6=0.0005

A: Given equation is f(x)=x2-4sin(x) Initial approximation is x0=3 Now f'(x)=2x-4cos(x) formula for…

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

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Q: 8. Suppose you have a function f continuous on [0, 2] given by πχ f(x) = x + 2 sin(- 3 (a) Show that…

A: It is given that,  f is a continuous function on [0, 2]  defined as ; f(x) = x + 2sinπx3-1 + 1 a) We…