Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,, f(x) = ах + b -1 1

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

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Q: n, ]x| fn (x) = - 2m 0, x > 2n | fn (x) cos x dx lim Calculate its limit. What happens if the limit…

A: Write the integral as limn→∞∫-11fnxcosx dx=limn→∞∫-1-12nfnxcosx dx+∫-12n12nfnxcosx dx+∫12n1fnxcosx…

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

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Q: Express the limit as a definite integral on the given interval. n lim x, In(2 + x,-) Ax, [0, 4] i =…

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Q: Express the limit as a definite integral on the given interval. n eši -Ax 4 + X; lim [0, 2] i = 1

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Q: Limit as x approaches 0 1-cos(x)/sin(x)

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Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &  ∆XYZ, ∠R≅∠X.

Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

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Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

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Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: Express the limit as a definite integral on the given interval. cos(x) lim Дх, [Зл, 4л] X; i = 1 dx

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Q: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: Approximate the length of the curve using n secant lines for n = 2; n = 4.y=ln x, 1>=x>=3

A: We have been given a curve y=lnx and we are supposed to approximate the length of this curve between…

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: An object hangs from a string in a stable position and is represented by the function y = 4 sin (3x)…

A: NOTE:Use the form y= asin(bx−c)+d to find the variables used to find the amplitude, period, phase…

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

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Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

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Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: Express the limit as a definite integral on the given interval. [2 - 5(x,")2 + 6(x,)³] Ax, [4, 8] n-…

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Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

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Q: 1- The point of intersection of the logarithmic functions on the X, Y axes =1. Why? 2- Are all…

A: As per the company guidelines we are supposed to solve first question only with its subparts. Kindly…

Q: 1. Find a root of f(x)=x-e=0, using Secant method, correct to three decimal places use initial…

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Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: Suppose that a drug is administered to a person in a single dose, and assume that the drug does not…

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Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Consider the given function as y=xlnx

Q: 5. Consider the function f(x)=e*, calculate df/dx with finite difference using forward and central…

A: We can solve this using formula of central difference and

Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

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: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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Q: At which points does f(x) = 2 sin x - cos 2x have an absolute maximum value and what is the maximum…

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Q: Express the limit as a definite integral on the given interval. cos(x;) lim n-0 i = 1 Дх, [2л, 5л]…

A: Given limn→∞∑i=1ncos(xi)xi∆xi in the interval [2π,5π]We need to express the limit as a  definite…

Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x, [о, 2л] (x, y)…

A: Given,

Q: Express the limit as a definite integral on the given interval. cos Xi lim Ax, [3π, 5π] 818 5m 3m dx

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Q: Express the limit as a definite integral on the given interval. lim 2 x;)?+9 -ах, [1,4] (x;")² + 9'…

A: Use;∫abf(x) dx =limn→∞ ∑n=1n f(xi) ∆x                       over the given interval [a, b].

Q: 2. Determine if the integral converges or diverges. Part of your grade on this problem depends on…

A: Topic:- integration

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

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