Find the inverse Laplace transform f(t)=L^(−1){F(s)} of the function F(s)=(2s^3−7s^2+32s−7)/[(s^2+16)(s^2+1)].

Q: Find the derivative of: h(w) = 3w + w^4/(2w^2 + 1)   [4w^5 + 4w^3 - 6w^2 + 3]/(2w^2+1)^2 [4w^5 -…

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Q: Given f(x)=(1)/(4)x^(2) how did we transform from the parent function?

A: Given f( x ) = 14x2

Q: dH f(5) = 8, f' (5) = 4 f(26) = 8, f'(26) = 6, g(5) = 1, g'(5) = -9, and H(x) = f(r² + g(x)). Find…

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Q: Find f'(x) if f(x) 9x (8x+2) 4 2√9x²-6 18x+48 5 (8x+2) 4 -9x² +16x+10 5 4(92²-6) 2 (8x+2) 4 6…

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Q: Find the inverse Lapace Transform    L^(-1) {1/[(s^2 +9)^2]}

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Q: Let f(x)=x^3 + 5. Explain why f(x) is invertible, then how all steps in the derivation of a formula…

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Q: Consider f(t)=. Find f'(1).

A: Given ft=<6t2,5t3,8t4> Differentiating the given function with respect to t, we get…

Q: Which expression to (3 + i)(1 - i)? Note i √-1. O4+i O 4 O2 - 2i O4 - 2i is equivalent

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Q: find the inverse Laplace transform of the given function of 4e^(-2t) / (s(s+4))   Thank you for…

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Q: Compute f’(-2) using shortcut rules. f(x) = 5x + 9

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Q: "Let T_3(x) be the Maclaurin polynomial of f(x)=e^x. Apply the Error Bound to find the maximum value…

A: Given that f(x)=ex The maclaurin series is, ex=1+x+x22!+x33!+....+xnn! Where, T3=x44!+...+xnn!+....

Q: If f(t)=(t^2+4t+3)(5t^2+6). find f('t) and f'(3)

A: Given: f(t)=(t^2+4t+3)(5t^2+6) find f('t) and f'(3) = ?

Q: 1. Find the derivative of the expanded function  a. a^2x^2+2abx+b^2 b.…

A: 1. a) Given, a2x2+2abx+b2 Consider,  y=a2x2+2abx+b2 Differentiate with respect to x,…

Q: If f (x) 2e²x Then compute f" (0) + 2f' (0) + 2ƒ (0)

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Q: Suppose f is an invertible function and f^-1 is its inverse. Explain how we can use the chain rule…

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Q: why is it f'(x)=(x^2+5)(1)-x(2x)/(x^2+5)^2  where did the (1) and 2x come from in the numerator?…

A: We have to explain the first order differentiation of the given function

Q: The moment generating function of X is given as follows: M(x)(t)= e^(8t). Use the moment generating…

A: It is required to calculate the mean of the random variable X, using the moment generating function.

Q: Let f(x) = e^x Find the polynomial H3(x) of degree at most 3 such that H3(1) = f(1), H3(2) = f(2),…

A: Given: Consider the given f(x) = ex .Using a (generalized) divided-difference table, find the…

Q: Find the derivative of f(z) = (x³ + 5)(z³ – 5) %3D (8z")(5x*) (8z +5)(z – 5) + (z³ + 5)(5x* – 5) (8z…

A: We need to use the product rule.

Q: What is the residue of the function f(z) = (z^2 + 1) / (z^3 - 2z) at the point z = i?

A: We have to calculate the residue at

Q: Let f: ℝ → ℝ by f(x) = 1 + x^2 and g: ℝ → ℝ by g(x) = 2^x + 3, calculate the following: (f ○ g)(1)

A: The composition of f and g is defined as:

Q: show that e^(4t-3t^2) cannot be a moment generating function

A: Moment Generating Function:                The Moment Generating Function is the expected value of…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.