lim (sin t)(In t) t→0+

Q: Vsinte-sinh²t, dt using 12. Find the leading asymptotic behavior as x tends to infinity of Laplace's…

A: Given the integral I(x)=∫0π2sinte-xsinh2tdt as x→∞  which is in the standard Laplace form…

Q: Show that each function in satisfies a Laplaceequation. ƒ(x, y) = ln√(x2 + y2)

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Q: sin TZ Let f (z) = Find the residue of f (z)at z = 3 (z – 3)2

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Q: 7. Evaluate using the residue theorem eir dx x2 +1

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Q: 1/a | sin(t")dt Find lim T.

A: We have to calculate the value of : limx→∞∫01xsint2dt·x

Q: 4) Verify the identity using the definitions of hyperbolic functions. e2x + 1 e2x – 1 coth x

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Q: Show that g(t) = t² tan t takes on the value for some t in [0, 4J.

A: Given Data The equation is g(t)=t² tan t. The interval is [0, π/4].   Put the value for t=0 in…

Q: sin TZ Let f (z) = Find the residue of (z – 2)? f (z)at z = 2 -

A: We have to find the residue of f(z)  at z=2

Q: find the given limits

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Q: f(x) = [sin x if 0 T

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Q: f(t) = cos(t/2) - sin(t), in the interval of [-T,1].

A: The given problem is to find the Fourier series expansion of the given periodic function with given…

Q: Evaluate using the result of Exercise 54

A: We use the half angle formula

Q: find the given limits

A: we have to find the limit limt→-1t3i+sinπ2tj+(ln(t+2)k

Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

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Q: Find lim t→ 1 1 - cos2 Int 0(0.20 를 를) 0 O t ./t+7, t-1 t2 − 1

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Q: Prove that for all x € [1, 00), – sinh (- |cosh¯'(x)|) = Vx² – 1.

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Q: -4t Find the indefinite integral dt and verify the result by differentiation. (t2+3)3

A: Integrate using substitution than take derivative to verify the result.

Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: 2 = using the relation r= VT show that sin x %3D EX II

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Q: Evaluate using the result of Exercise 54

A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

Q: 1+ In x Find f(x) so that when u f(x) the integral tan( fx) dx can be rewritten as cot u du. A) x-…

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Q: b. b-a Use the equation fte)dx = lim ** ) to evaluate the following definite integral. n-0k=1 2 |(2x…

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Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: Fundamental Theorem: 2x sin t -dt. Find the value of f'(x). t2 +1 Let f(x) = | %3D

A: We can solve this as follows:

Q: Let f: (−π / 2, π / 2) → R be given by f (t) = tan − 1 (t). (a) What is Taylor's polynomial P1 (t)…

A: Consider the given function. Find the derivative to determine the first order of the Taylor's…

Q: ) 3x - 4x= sin社 ; at t=0,x==

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Q: Let f(x) = tan x. (a) Find the linearization of f(x) at x = (π)/(4).…

A: Given that the function: fx=tanx…

Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

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Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: 1/a (e) lim (1– sin(z))/=

A: When limit is of the form 00 or ∞∞ , then L'Hospital rule is used.In this rule, we take the…

Q: sin TZ Let f (z) Find the residue of f (z) (z – 3)² at z = 3

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Q: Verify Initial and Final value theorem for the function. f(t) = 2 + 3 cos t.

A: Given function is ft=2+3cost. We have to verify the initial and final value theorem. Initial value…

Q: sin 7Z „Find the residue of f (z)at z = 4 (z – 4)? Let f (z) =

A: Note:

Q: - [² Suppose F(x)= = sin(t) dt. Use the Fundamental of Theorem of Calculus to calculate - (F(x³)).…

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Q: let h (z) =(arcsin(5z)+ln(4-z))^27. find h'(z)

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Q: lim x" sin is NOT zero when: x→+∞ O a 1 a > 1

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Q: Find the limits sin(3t) lim In(sin(3t)) i+ In(tan(4t))" j+tln(3t) A t→0 sin(4t)

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Q: Q2) A: If u = sin-()+ tan-(), prove that du ди x=+y дх ду = 0 ax ay n lim (1+ (1 + iV3)10 B: Find:…

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Q: II. f(t) = cos t, lim h

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Q: sin TZ Let f (2) = Find the residue of f (z)at z = 3 (z – 3)?

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Q: 43. lim (sin t) (In t) t0+

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Q: lim-sin t t0 In(2et_1) %3D A © D B.

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Q: If f(x) = A B C D tanx S 0 sec²x √1+1² 1+e¹ -dt, then f'(x) equals 1+e tanx In (secx)√1+tan²x 1+ e…

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Q: In (tan (x)) dx. 3. Evaluate J sin(x) cos(x)

A: NOTE: Refresh your page if you can't see any equations. . ..............(1) substitute  take…

Q: HiW Q Prove that : tanhclax) = x-! %3D x2+1

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Q: 5. Given F(x) tan(t) dt, evaluate F(0) and F'(0). 1+sin(2x) 1+ et-1

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Q: Limit as t goes to 0 of    (t^3+3t) / sin (5t)

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Q: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

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Q: (a) Evaluate the integral t tanx dx by using the reduction formula of tangent function.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.