Find a potential func A potential function

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Q: (a) Show that arctan z = log ( ) in the sense of multi-valued functions. Hint: show that w = log )…

A: To find - Show that arctan z = i2 log1 - iz1 + iz in the sense of multi-valued functions. Hint :…

Q: ntegral Sa F . 0) & (1, 1)

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Q: sinx Prove that lim 1|

A: Solution: Consider the given limit function and we have to show that  limx→0sin xx = 1 So, limx→0sin…

Q: tan Evaluatee 8 sec dv. tan 8 sec e (Use C as an arbitrary constant.)

A: The given integral is

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g'(s) Need…

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Q: lefinition of the derivative o

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Q: Qs:- Prove that fez) = cx-g') + ( are harmonic function of (xy) ,but not hormonic conjugates.

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Q: | cosh(In z) dr

A: Given:  Let I=∫1e coshln x dx To Find: To evaluate the given integral.

Q: equation with the appropriate slope field. y' = x-y 11

A: Show slope field on graph

Q: Exercise 2. Evaluate f'(-T/3) where f(x) = = cos-(cos ). Be careful this one is little tricky.

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Q: 1 Use the fundamental theorem of calculus to find the derivative of g(x)= | dt. +1

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Q: Estimate `sin(-0.01)` using an appropriate linear approximation L(x) = f(a) + f'(a)(x – a).…

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Q: Sketch a potential f(x) given the following graph of the first derivative f'(x). Explain you…

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Q: How can substitutions in single definite integrals be viewed as transformations of regions? What is…

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Q: sec³ x sin x dx (Hint: factor out cos? x) Vcos? x + sec x

A: Consider the provided integral, ∫sec3xsinxdxcos2x+secx Solve the integration by u substitution…

Q: find the derivativeof the transcendental function. \text { 44. } f(\theta)=(\theta+1) \cos \theta

A: fθ=θ+1cosθ

Q: cosi in the form x+iy %3D

A: On solving,we get

Q: Show that the function F= the fallowing canohical tranformatione %3D COS and %3D

A: Determine q from Q=ln1+qcosp and then express q and P in terms of p and Q.…

Q: 7 f(x) dt 3

A: Given that, f(x)=∫3x2(t23-1)7dt Now, the fundamental theorem of calculus tells us that If…

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: Given

Q: 15 Using Part I of the Fundamental Theorem of Calculus, evaluate: da tdt =

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Q: te its joint PDF. derive its CDF from the PDF.

A: From the given information, The uniform distribution can be defined as:

Q: -e-atp" dt =

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Q: olw) - " ir Use part one of the fundamental theorem of calculus to find the derivative of the…

A: g(w)=∫0wsin7+t5dt The fundamental theorem of calculus is ddx∫0u(x) f(t)dt=f(u(x)).ddxu(x)

Q: () Use part I of the Fundamental Theorem of Calculus to find the derivative of 17 F(x) tan F'(z)=…

A: Topic-  derivatives of definite integration

Q: sinhz analytic or not ?

A: The given function is fz=sinhz. A function fz=ux,y+ivx,y is said to be analytic if the first partial…

Q: liminate the parameter

A: Given: a) x=tan t and y=sec2t -1 b) x=t+1 and y=1t+1 To eliminate: The parameter.

Q: Area under a curve

A: Let us consider the equation of curve be y = f(x).Let us consider two data points x = a and x = b,…

Q: dt Use the Fundemental Theorem of Calculus to find the derivative. dæ 8+ Vi

A: Given : ddx∫0xdt8+t

Q: Find the derivative. (The Fundamental Theorem of Calculus- Part 1) 19) у %3D cos /t dt COS

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Q: Exercise 2: Derive the formula for the derivative of arcsec(x) in two different ways: (a) Let…

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Q: 1. Use the fundamental theorem of calculus part 1 to compute the derivative VI-t²dt. cos(z) dr

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Q: Explain the concept of Newton approximation. Present the idea in general and illustrate it using…

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Q: Explain First Shift Theorem & its properties?

A: First Shift Theorem: If Lft=Fs, then Leatft=Fs-a. The proof of the First shift theorem follows from…

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Q: a) Expand Sinx by Maclaurin's Theorem.

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Q: 79. Proof Prove each differentiation formula. d (a) -u' dr larccos u] V 1- u?

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Q: State De-Moivre's theorem. Compute n" derivative of the function y th x² +a?

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: a) = Cos(x + a); prov

A: we have ,  sin(x-α)=cos(x+α)we have to prove that, tanx=1

Q: By the Fundame 2+x? dx. 1

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Q: What ae the Singularity Functions?

A: A singularity is a point at which a function does not possess a derivative. In other words, a…

Q: Find Derivative Using Fundamental Theorem: 1. Use Part 1 of the Fundamental Theorem of Calculus to…

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Q: Q/ By uesing chain rule Find du - de For this functions ?

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Q: Define cumulant generating function. Obtain a relationship between cumulants and moments.

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Q: sinh(1 + iπ/2)

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Q: Evaluate the definite integral dx | using Part 1 of the Fundamental Theorem of Calculus. Remember to…

A: ∫01 10x4-21dx =∫0110x4dx-∫0121dx =10·∫01x4dx-∫0121dx

Q: Verify the derivative of nature logarithm (use the formula of In). d u' -[In\u] = dx и Verify the…

A: Given a formula,