Question 2: Verify the following: e-as (a) L{u(t – a)} =. F(s) = L{f(t)}. (b) L{f(t – a)u(t – a)} = e-a$ F(s) where

Q: Question 1 [- Let f(x, y) =ln(xy)-50x³y Find fx, fxy and fxyx.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Example 5. In the bending of an elastic beam the normal stress y at distance x from the middle…

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Q: Question 17 1 Point Evaluate: / (3*-e") de A (3-e)*. In(3-e)+C e*+1 +C x+1 3*+1 x+1 3* -e* +C In (3)…

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Q: 3. Evaluate in terms of gamma function: T'e

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Q: Question 4. Reduce the equation Uxr + Uyy - 2uz + 4uy + u = 0 into the form Vrr + Vyy +cv = 0 =…

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Q: Example 4.2 Given that L{f(t)} = F(s) = e stf(t)dt, prove the First Shift Theorem: L{e-at f(t)} =…

A: Here given that                        ℒ{f(t)}=F(s)=∫0∞e-stf(t)dt .........................(1)…

Q: QUESTION 11 Let X denote the time to failure (in years) of a certain hydraulic component. Suppose…

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Q: Question 19 * 19. Differentiate f (x) = 3 ln (2x –1)´ with respect to x . 12 S"(x)=- 2x-1 A S'(x)=:…

A: Given :f(x)=3ln(2x-1)2

Q: Evaluate in terms of gamma function: x°e-3¤ dx O r(7) Or(17) O(7) OI(7)

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Q: a n п i = 6 dz EVALUATE IN TERMS OF GAMMA FUNCTION.

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Q: Question 4: Solve the equation ë + 6¢ + 8x = g(t), where g(t) is an impulse of 4 units applied at t…

A: Lxt=Xs,L-1Xs=xt d2xtdt2=s2Xt-sx0-x'0dxtdt=sXt-x0 L-1Xs=xtL-11s=1L-11s-a=eat x¨+6x˙+8x=gtx0=0,x˙0=3…

Q: Question 12 If L{f (t) }= | e-(s+1)! ¡2sin²4 dt_then what is f (t)? ,- (s+1)! ¿2sin²t dt, then what…

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Q: 12 d Using Part I of the Fundamental Theorem of Calculus, evaluate: dx t? dt =

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Q: Chapter 23 | Implicit Differentiation and Chain Rule 1. Find dw/dt given w = 5 cos(xy) – sin xz, x =…

A: Here the given equation is w=5cosxy-sinxz, x=1t, y=t, z=t3.

Q: 10. a. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the functions:…

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Q: Problem 17. Suppose that F(x) = = [₁,²50 Find F"(2). f(t) dt, where f(t) = 1 ² √² + 1² VT U - du.

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Q: Problem 8.1.3. Prove Lemma 8.1.2. Lemma 8.1.2. / and are integroble functions and a < b.mem then |…

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Q: Question 1. Find the linearization of the function y = f(x) = x² sin(x) at a = T/4 and use it to…

A: Linearisation of f(X) at a is given by-  L(X) = f(a) + f'(a)(x-a)

Q: Question 11 A те *dz is A в D E) divergent

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Q: 7. If aatiß = (x + iyy*4, a>0, prove that %3D (i) a = 5 log, (x + y) -q tan log, e- loga (r + y) =…

A: The given isaα+iβ=x+iyp+iq,a&gt;0.prove thati α=12logax+y-qtan-1yxlogaeii logax2+y2=2αp+βqp2+q2

Q: s+2 (s+4s+5) Inverse laplace of

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Q: QUESTION 5 The approximation of x e*dx by Simpson's Rule is 0.160602 O 0.160603 O 0.162402 O None of…

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Q: Question 2 Let r, y ERt with x < y. Show that y-l<x-1.

A: We have to prove that the given inequality.

Q: Question 10 Let F(x) = (3t2 - 3)dt then F"(1) is equal to: %3D 6.

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Q: QUESTION 11 dz = = zP z1- -i (-e2 – 1)i e (e? + 1)i e (e? – 1) ei (e2 – 1)i e

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Q: alpha iõtä 100 rhô 2 beta 20 kappa 200 sigma K 3 gamma 30 lambda 300 tau 4 delta 40 mu 400 upsilon 5…

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Q: Question No. 5) Use Laplace transform to solve y"+3y' + 5y = 3, with y'(0) = 2 y(0) = 1,

A: Given differential equation is y''+3y'+5y=3 Taking Laplace transform on both sides, we get…

Q: 1 D = | (1+e*)³e' dt -1 E t In (t) dt 2 1 F In ( 1+ dt 1 G = t² In3 (t) dt 1

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Q: Question 5 What can you derive by applying Associativity (Assoc) to F~O • X)

A: In the given question, the concept of associative property is applied. Associative Property The…

Q: EXAMPLE 1 Find an antiderivative for each of the following functions. (a) f(x) = 2x (b) g(x) (c)…

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Q: e 8(t – 3) dt = e^15 cos(31)6(t – 5) dt =

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Q: QUESTION 3 Let f: R → R be the Dirichlet function (f(x) = 1 if x EQ, and 0 otherwise). Define A to…

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Q: Question 15 Write a chain rule formula for the following derivative. for w = f(x, y, z); x = g(s,…

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Q: Зх- 1 | (*-9) dt Use Leibniz's rule to find for y = dx

A: Leibniz's Rule:ddx∫a(x)b(x)f(x,t)dt = f(x,b(x))·db(x)dx +  f(x,a(x))·da(x)dx - ∫a(x)b(x)∂f(x,t)∂xdt…

Q: Sheet 4 Numerical analysis dx QI/ Evaluate Jo 1+x2 Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: In the question we have to find value of integrals.

Q: Question 02 Suppose that w = / x2 + y2 + z², (1) x = cos 0,y = sin 0,z = tan 0 (2) Use the chain…

A: Given,           w=x2+y2+z2 , x=cosθ , y=sinθ , z=tanθ           When θ=π4

Q: ylo) >3 y'lo) : -s g"Co) » 1 y" Co) = -23 yu Co) = 47

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Q: Question 1 d dx Jx & S" cos(t) dt = O a) cos (x2) · 2x b) cos (x²) · 2 O c) sin (x²) d) sin (t² ) e)…

A: topic - integration and derivatives

Q: 10 Using Part 2 of the Fundamental Theorem of Calculus, evaluate: d t*dt = dr

A: I have provided solution in step2.

Q: 1.5 Approximate f x*dx using Simpson's rule Select one: a. -1.3190104 b. 10.3190104 c. 1.3190104 d.…

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Q: 1. SF ·d† = 0 2. ,F ·dT >0 3. ,F ·dT < 0 4. The value of [, F ·dT cannot be determined with only…

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Q: 1.5 | Example 8.26. Evaluate e- J0.2 dx using the 3-point Gaussian quadrature.

A: Given: Let us consider the given equation, ∫0.21.5e-x2dx. Determine the given using the 3-point…

Q: 8 4) The inverse Laplace f (t) if F(s): %3D s2+2s+3

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Q: 10 [s(s+4)(s+5)²

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Q: Question 16 * 16. The derivative of the function h(x)=In(1–3x)is 3 = (x).4 1-3х A B…

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Q: Question 10 x²+x+1 Ja 2x²+2+x³+x So - dx = [Aƒ (x) – B ln(g(x)] + D fb dx, and if A = ,B<0, then…

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Q: Question 18 Evaluate: fo S, e dy dx O e - 1 O ve

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Q: II EIN ep %3D 4-cose .A 15 .B V14 13

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Q: Question 16 d If g(x) = == S[e²-In (21+1) ]dt, find g(x). dx 4 A et + (2x+1)2 e* -In(2x+1) 4 e¹+ (2x…

A: We will first find g(x).