Consider the time series x, =0+1z,, where z, - WN (H.a) and 0 is a real valued constant. (a) Calculate: (i) E(x, ).

Q: Differentiate: f(x) = 2ª + e² + log, 5 f'(x) = 2" In 2+ e² A 1 ® f'(x)= 2" +e² + : 1 © f'(x)= 2" +…

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Q: Estimate n such that V * log(x) dx – T₁| < 10-8. Tn

A: for the function f(x)=logx  To find the value of n so that the error bound in trapezoidal and…

Q: Q1 Let X1, .. ,X, f(r;0) = ()0 (1 – 0)2-, x = 0, 1,2. (i) Show that f(x:0) is a member of the…

A: It is an important part of statistics . It is widely used .

Q: If f(x) = log,(cot(x) + a?) , then f'(x) = %3D (A) 1 (cot(x)+2?) (B) csc (x)+2x (cot(x)+r) 1 (C)…

A: By using differentiation formula and change of basis formula, we calculate the derivative of given…

Q: The domain of the logarithmic functiort f(x)=log_(a)x is

A: We find domain of the logarithmic function f(x)= logax.   Where, a &gt; 0 is a constant.

Q: Find a function f(2) such that f (x) = e + 7x and f(0) = - 1 f(x) =

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Q: (a) Use the definition of L{·} to determine L{te=#}

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Q: 2. If j is the rate of simple interest for the k-th period of time, where k = 1,2,..., n, show that…

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Q: 15) log.(x + 4) + log,(x - 2) = log,(4x) %3D

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Q: 6) Consider the exponential function f (x) = ex* [C:4] a) Determine the n-th derivative of f(x). b)…

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Q: et f'(x) = with the initial condition f(1) = 5. Determine the particular f(x).

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Q: A company estimates that its sales will grow continuously at a rate given by the function s'() =…

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Q: A) Differentiate y = 4Vx +- + 10 8 B) Find the second derivative of y = 4Vã + + 10 C) Find the…

A: As per our guidelines  we can solve only  3 subparts of a question . The rest can be reposted.  In…

Q: A(t) = 3000e027z initial investment of 3000 dollars which pays 2.7% compounded continuously. a) Find…

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Q: Find the Maclaurin's polynomial of degree 3 for ( a) f(x)=(1+x)e²*

A: Maclaurin Series of f(x) of Degree 3 is : f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: or formula (**). (Answer: (a) Let f(x) = x² – 3x + 2. Find f'(4) using either formula (*) 5)

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Q: Find f'(1)when f(x) = ln(e*x").

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Q: By= In(Cx-2)

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Q: Find f'(z) of f(z) = Log(z2i).

A: Given complex function is  f(z)=log(z2i)

Q: The graph of f is given to the right. Let g(x) = f(t) dt. (a) Find g(3). (b) Find g'(-2). (c) Find…

A: Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: 3. Differentiate. x²e* f(x)%3= x² + ex

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Q: Let F(2) = 2, F'(2) = 3, H(2) = 4, H'(2) = 3. A. If G(z) = F(z)*H(z), then G'(2) = _______ B. If…

A: The Product Rule:The Quotient Rule:

Q: 2. The population of a certain species of bird in a local sanctuary, P(t), t years after 2020 is…

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Q: Let f(x) = – 51log, (x) f'(x) f'(6) =

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Q: 2x 5. F(x) = "(5t – 1) dt

A: Here, it is given that F(x)=∫x2x5t-1dt

Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

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Q: Sxg'(x) + g(x)f"(x}] dx = f(x)g(x) + C° %3D

A: To prove the following formula.∫fxg'x+gxf'x dx=fxgx+C