Confirm that the standard Fourier forward transform of the double-sided decaying exponential signal (:) =. is F(@)=- 2. where a is a positive constant and = --H t>0 , tso'

Q: Find the 55th derivative of (1 + x²) 28 at x = 0.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 1/x h(x) =…

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Q: y = log (cos(2x) );y'=* %3D %3D O 2 tan ( 2x ) / In (10) O - 2 tan ( 2x ) / In (10) O 2 cot ( 2x ) /…

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Q: Prove that f(x)=log(x)-x^2 +1 has exactly two roots namely x=1 and x=0.45

A: Function: f(x)=log(x)-x2+1 If it has two roots x=1 and x=0.45 then f(1)=0 and f(0.45)=0.

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

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Q: Write down the characteristic equation and find the general solution to x'' - x' - 2x = 0.

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Q: a) Use Logarithmic differentiation to take derivative of y = f(x) = (x)ª cos² x (x3+1)3

A: We use Logarithmic properties

Q: use logarithmic differentiation to find the derivative

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Q: A B C D E F f(x) X

A: To determine the points at which exactly two of fx, f'x and f''x are zero.

Q: What is the third derivative of f (x) = a + cosæ?

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rx 5 g(x)…

A: Step 1:Step 2:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

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Q: Show that the derivative of ! log (9-1)(g-1)u²+2u–1 u e [0, 1], q 2 3 > 0 for u > 1+(q-1)(2–u)u

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Q: Find the inverse function of f(z) = 4 + V7. f"(z) =

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) =…

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Q: 6) prove that cost '2 = log (2 + √2²-1).

A: To prove that cosh-1(z) = log(z + sqrt(z2 - 1)), we can start by defining the hyperbolic cosine…

Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

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