Verify Cauchy's MVT for f(x) and f'(x) in [4,9] where f(x) = Vx %3D

Q: Find the derivative of In(3t³ – 2t + 1) and then calculate S; + 3 dt (use integration by…

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Q: Find the Integration of: fn (3sint + esin t) cost dt In 3

A: Given that, ⇒                   y =∫π2π( 3sint +esint) costln3dt⇒                     find the value…

Q: Use order of h® Romberg integration to evaluate xe2x dx

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Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: 1 Prove that the integral : Tz dx is convergent. 1+x

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Q: Find the average value of f(x) = sin³ x cos³x on the interval [0,1].

A: We need to find average value.

Q: Determine whether the improper integral diverges or converges. dx 1. (2х-1)3 dx 2. x +1

A: No.2 The improper integral is of second kind where f(x) = 1/(x+1) has one point of infinte…

Q: 19) Derive a one point integration formula to estimate the integral f (x) dx.

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Q: (a) Evaluate the indefinite integral (anti-derivative) d.x Vr2 +1 by using the substitution u = x?…

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Q: Compute the second derivative of  f(x)=ex+x  at x = 2 using a step size h = 0.2  The backward…

A: According to the question; f(x)=ex+x                                                     ; x=2step…

Q: Determine whether the improper integral diverges or converges. dx 1.So (2x-1) 7 dx 2. x +1

A: We have to determine whether the improper integral ∫-17 dxx+1 diverges or converges.

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 third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

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

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: The forces of the human gastrocnemius tendon during traction and during recoil can be approximated…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: Determine whether the improper integral converges or diverges. V5x + 8 dx x2 1

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Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the…

A: Given

Q: Find the derivative of F(x) = 4 n sin(t) dt. %3D dx 3x² cos(x)

A: Integral calculus is one of the two main parts of calculus that is concerned with the study of…

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

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Q: The improper integral 1 dx converges to '5 Vx-5

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Q: An odd piecewise continuous function f(x) on every finite interval of (-0, 0) such that / fx)| dxis…

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Q: Determine whether the improper integral diverges or converges. dx 1.Lo (2x-1)*

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Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

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Q: Find partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

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Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: .2 x+15 dx Jx* +3 1

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Q: Calculate the second-order partial derivative of f(x.v) =sin(x³v?) with respect to x and y, that is,…

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Q: : Evaluate fxe dx to using Romberg integration to an error of order

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Q: F(x) = x · S, 2e' cos-lt dt at x = 1 In x

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Q: Determine whether the improper integral diverges or converges. dx 1.fº. (2x-1)3

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Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

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Q: In 3 | (1-x)e"dx ах In

A: Consider the given integral

Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…

Q: et * e-t Compute the convolution integral.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: