The function g(x) = ln(x³ – 1) defined on V2, 0) is not zero unless x 2.

Q: Find a function f € span(1, cos x, sin x) which minimizes the integral 2πT √²* |x +1 − f(x)| ²dx.

A: Given a function                     f∈span1, cosx, sinx

Q: Find the differential d4y of the function y=x5.

A:

Q: Find the derivative of y with respect to x. y = tan (In 3x) O A. 1+(In 3x) 21 O B. x(1 + ( In 3x)) 1…

A: Given: The function y=tan-1ln3x, To determine: The derivative of y with respect to x,

Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

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Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: Find the linear approximation of f(x) = lnx at x = 1 and use it to estimate ln(1.02). L(x) =…

A: Given that: f(x)=lnx

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: Find the linear approximation of f(x) = ln x at a = 1 and use it to estimate In(1.2). L(x) = In(1.2)…

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Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: 17. Consider f(x) = dt. DO NOT state that f(x) = In x but explain how it behaves exactly like the…

A: In the question we need to evaluate the integral.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

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Q: Use Part 1 of the Fundamental Theorem of Calculus (and properties of definite integrals and the…

A: Solve the following

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) =…

A:

Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

Q: Find the linear use it to estimate ln(1.44). L(x) = In(1.44) approximation of f(x) = In x at x = 1…

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Q: Find values of p for which integral diverges. dx x(In x)"

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.34). L(x) =…

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Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

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Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Suppose that x and y are both differentiable functions of t and are related by the given equation…

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: Find the general form of the antiderivative of g(x) = - cos4x

A:

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = er+1) 3- xy +x*y = 3 at x = 1

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

Q: Find the differential of the function f(x) = (x+4)^(1/2) dy =

A: Find the differential of the functionf(x) = (x+4)^(1/2)

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

A:

Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: dz +y ay dz 100 z= log ( x 100 + x50 y50 + y100 ), Prove that x

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: Determine the expression of the integrating function if it is known that: e) S; f(x)dx : - sen(9) +…

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Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

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Q: Find the general antiderivative of f (x) = 4 x ln x²

A: Given: fx=4xlnx2

Q: prove using the IVT. e^x + ln x = 0 has a solution.

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Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

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Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

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Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

A: