Ir f(t) = {* S VE – 1, t>1\ t >11 , then L{f(t)} = 0, t <1 [ O a) VTe-s s1/2 Ob) Vre s3/2 c) Vne-s 2s3/2 d) 2(s+1)3/2 O e) None of these

Q: (b) Prove that the improper integral Ï Ï -8 -∞ converges. dx dy (1 + x² + y2)3/2

A: Consider the given improper integral, I=∫-∞∞∫-∞∞dxdy1+x2+y232 Change into circular coordinates by…

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A:

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

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A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: f(x) = 1+x tan? r is f(x) uniformly continuous on [0, +o0)? Prove your result.

A: TheoremIf f:[0,∞) →R Be continuous on[0,∞) and limx→+∞ f(x)=0, f isuniformly continuous on…

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Q: dx 3) L. Vx+1

A: Given:

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Q: actuaZ D X=Ytmacking weigh Şk.(i-cx-3)³), ifɔ 147 f(x)= 0, otherwise (4) k=? SFxsdx=1) →1=…

A: Given, the PMF, fx=k1-x-32, 2≤x≤40, otherwise

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A:

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Q: Let f : [0; 1] --> R be a continuous function with f(1=4) = 2. Dene F(x) = integration from 0 to 1…

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Q: | de P8- メレー Oe dedx

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Q: /tangent slupe rosin (20) when dy ス 5. 555 653 3. not of thc above

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Q: x° sin(x³) In(4 + cos(x³)) if x 10° ya. 00 Determine whether or not the improper integral dx…

A: We have to use comparison test here.

Q: Q: Find a continuous function f (x) satisfying x*– 4x'<f(x)<2x -x' for all x e [0,2] such that the…

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Q: Evaluate in terms of Gamma function: y^5√(b^2 – y^2) dy LIMIT: 0 to b

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Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: Find the absolute extrema of the function on the closed interval. y = 5 cos x, [0, 2n] minimum (x,…

A: Solve the following

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

A: Topic:- integration

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A: According to the condition of convergence for Fourier integral,  Let f and f' be piecewise…

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Q: x3 + x 9) (8.7) Find the integrals convergence and its value | zdx. x3

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Q: 2″ Given f(x) = xr-¹e-λx, x > 0, r, λ > 0. Γ(r) 2. Evaluate etx f(x) dx. HINT: Express f etx f(x) dx…

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Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…