Theorem 13: If f(t) has a continuous derivative and is of exponential order y for large positive values of t, where y>0 and if L[f(t)]= ƒ(p) then L"[f (p)]= f(t) is given by

Q: 3) Differentiation D: F[t] ---> F[t], is linear and satisfies Dt¹ = nt¹-1. It satisfies the usual…

A: (a) We have f(c) = 0 if and only if (t-c) divides f in F[t]. Thus, we can write f(t) = (t-c)g(t) for…

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

A:

Q: Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is…

A: To show that the given function ft=sinet2 is of exponential order.

Q: 5. Consider the function { Va if 01 f (x) = What is the derivative function for f(x)? What is the…

A: The given piecewise function is  f(x)=xif 0≤x≤112x+12if x>1

Q: 1. Let f(x) = Ve-r. Find the second derivative of f(x) with respect to r. For which values of x is…

A:

Q: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

A:

Q: - 3x Find the derivative of y with respect to x if y = e

A:

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Let F be an anti-derivative of the function x+(1/x)  for x≠0 such that F(−1)=1. If you think that…

A: Suppose F be the anti-derivative of the function x+1x, then Fx=∫x+1xdx

Q: Suppose the function f and its derivative ƒ' have values as given in the following table. f(x) f'(x)…

A:

Q: Suppose f(x) is a function that satisfies the following conditions: f(15) = 20, f' (15) = 2. Also…

A:

Q: 1. Find the derivative of the given function: (a) f(x) = log(1+x²) (b) g(x) = e+sin x arctan(cosx);…

A:

Q: If a function is defined by an equation G(x,y)=0 and could be found explicitly as y=f(x), then the…

A: We have to check

Q: 10. Find the derivative function for f(x) = √ x + √x + √x + √x + ... √ + +....

A:

Q: 1. Consider the error function, erf(x), defined by erf(x) = e-* dt. This function is important in…

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

Q: 2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D…

A: Given that, f(x)=x2ln x +1 To find f''(1) when h=0.2 Using second derivative formula,…

Q: 4. Find the derivative of each of the following functions. (a) f(x) = (x? – Va) - e* (b) g(x) c+ re

A:

Q: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: Draw the graph of any function f(x) for which the derivative at 0 exists and equals 1, ie f'(0) =1.

A: Given, f'(0) = 1

Q: 5. Find the derivative of the function f(r) = (r² + 5)e %3D

A:

Q: Verify that each of the following difference approximations for the first derivative provides the…

A: As each approximation has independent of previous one . So according to guideline , I am verifying…