R² and r are defined by SR E(*; – T)(yi – ỹ) Say R? SST' r = VE(x; – #)² L(yi – g)² (1) Show R² = p2. (2) Define \ as E(yi – 9)(ŷ; – ) - - Show X² = R². (Note that ĝ = ŷ)

Q: f'(x) = V= and f(1) = 3- I|

A: Explanation of the answer is as follows

Q: If g(t) = (√t 4) (√t + 1), then: g'(4) =

A:

Q: Consider the function y = 2e4. Which of the following statements is true for y? O y'=y Oy = /v O…

A: given,

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A: We have to find

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A: Given that:f(t, p)=(pet+1-p)n

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A: We have to find out the Laplace transformation of f(x) = cos

Q: Q3. Find y= fx) such that y

A:

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A: Here we have to evaluate for a) and b) the value of f'(x).

Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

A:

Q: 11. Given the graph of fon the following page, determine the signs of f'(x) and f"(x). -4- -2

A: From the given graph :                              We can see that the graph is  a decreasing…

Q: a) If f (x) = 12x, find f' (27). %3D

A: Solve the function

Q: 2. If g(x) = (ƒ 03ƒ •4f)(x) = ƒ (3ƒ (4ƒ(x)). Determine gʻ(3), given f(3) = 1, ƒ(4)=1, ƒ'(3) = 2 and…

A:

Q: Let f(x) = sin(4g(x)). Evaluate f'(x).

A:

Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

A:

Q: [2, 03 b) If f(t)={ , find L{S(1)}.

A:

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

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A:

Q: Use the Rules of Logs to expand, then find f'(x) given f(x) = ln V. ex X (x + 3)5

A:

Q: 4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y-3y = 10 sinh 2t,…

A: Laplace transform.

Q: Let f(x) = X x - a Find the value of a so that f'(1) = 1 - 4

A: This question is based on Quotient rule of differentiation.

Q: 13. Use a u-substitution to evaluate /x²/(x³ – 2) dx

A: