t) := inf{a > 0 : wf(a)

Q: f (t) = 3e" cosh (In 2r -2t

A: Given,                 f(t)=3e-2tcoshln2t

Q: L{f(t – a)u(t – a)} = e¬as F(s) |

A: Topic:- Laplace transform and it's properties

Q: f (t) =1*b +acosh 21 + bsinh 21 a+b

A:

Q: Suppose f(x, y, z)=x+y+z, h(x,y) = (x + y, x³, y) and g(x) = (x,x²). Calculate d =z=of oho g(x). dx

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Q: 15) Consider the vector field F (x, y, 2) = (In y, x, z) and the oriented curve C:r (t) = (t, e', 2…

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Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

A:

Q: Is the function F (x) = L", e“ dt concave (concave down) or convex (concave up) for x<0?

A: To solve the following problem

Q: Suppose f, g:C → C are differentiable. Prove that fg is differentiable and that (fg)' = f'g + fg'.

A:

Q: Let f(t) be a continuous function with f(0) 5 and f(4) = 3. Compute F'(2), where cx² F(x) = [" .…

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Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

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Q: 6. Show that f(x) = sin x is uniformly continous on R.

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Q: Given F(x) = : (1–V1- (1+ 1)² ) dt Evaluate F(0) and F'(V2).

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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: dz (c) If z= f(x,y) where x= 6(t) and y=w(t) then write the rule to evaluate dt without…

A: We will find out the required value.

Q: Let u(t)=6t3i+t2−4j−5k and v(t)=eti+9e−tj−e9tk. Compute the derivative of the following function.…

A: solve the following

Q: If I let f(x,y) be continously differentiable, how do I prove gradf = (fx, fy)?

A: (.)  Let  f(x,y)  be a continuously differentiable function. (.)  Gradient of a function  'f' is…

Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

A:

Q: Find He valve of fe2) when fg functions such that are dilferentrable %3D g(x) >o 1 for all x, while…

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Q: If f(x) is continuous on a, b] thenF(x) = So f(t)dt is continuous. OTrue False

A: We need to check whether the given statement is true or false

Q: f(0) = 1 ise f(1) =? S xf'(x)dx = 2x³ + 2x² + c , 4 - O A) 7 OB) 5 O C) 8 OD) 10 O E) 15

A: