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

Q: 2. Prove that a) the function f(x) = tan x+x can be replaced by g(x) =x if x→0. b) the function…

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Q: Find ♬ as a function of x and evaluate it at x = 0, x = π/6, and x = π/2. -["sin e de Ꮎ F(x) F(0)…

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: If f is analytic in a neighborhood of xo and f(xo) = 0, show that f(x)/(x – xo) is analytic in the…

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Q: (a)Verify Rolle's Theorem for f (x)=x - 16x+10 over the interval [0,4].

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Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: а. f (x) 3D x(4 — х)8 b. y = x² – ? 2 С. у %3D In (x + 1) — tan-1

A: Critical number

Q: Find the absolute maximum and minimum of f(t) = -2cos2t + sin4t on  the interval [0,pi/4]

A: The given function is, f(t)=-2cos2t+sin4t and the given interval is, 0,π4. Obtain the value of the…

Q: Let f(x) = ri- 2xi.Find the value of c that satisfies the conclusion of Rolle's Theorem forf on (0,…

A: The graph is shown below:

Q: Prove that there is no function F that is differentiable everywhere and also satisfies the equation…

A: Give function is fx2+sinx=x we differentiate it, f'x2+sinx2x+cosx=1⇒f'x2+sinx=12x+cosx f'x2+sinx…

Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.Find any x-intercepts of f(x) on [0, 2π]

Q: Consider the following functions: (i) z = arctan (-) -(√) (ii) z= In (iii) z = (ex-ex) sin y. Which…

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Find the local and absolute maximum and minimum values of f(x) f(x) = cos x, x ∈ [-3pi/2 , 3pi/2

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Q: f(x) = = {2³² (sin ¹ + cos2) z € (-1,0) U (0,1] 0 x = 0.

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Q: y), the harmonic conjugate of u. Form the

A: A function u (x, y) is said to be a harmonic function if u _x x + u_ y y = 0.

Q: What is the domain of f(x)=Dsin1(IIn(x)l)? %3D Select one: O (0,e] O (0,00)

A: Given, fx =sin-1lnx  We have to find the domain of  fx =sin-1lnx

Q: The real part of an analytic function f(z) where z = x + iy is given by ey cos (x). The imaginary…

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Q: Suppose that f: R R is everywhere differentiable and that f'(x) 1 for all real numbers x. Prove that…

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Q: 1. (a) Draw the graphs of the functions x and x in the plane. Then find all integers n > 2 such that…

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Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: (c) On [0,27) the maximum values of the function occur at what x-values?

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Q: 1. Let f(x)= x on the interval [-7r, 7T. (a) Compute f42, given by 1/2 -T

A: To compute the L^2 norm of the given function, following the definition of the norm

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.