t 1 (17) = { { + ¹ t 0 1 1 F(s)= = =+ = /201 5² = 1+t-e¹-2(t-e¹-¹)μ(t-1) = 1+t-e¹-2(t-et-¹)μ(t-1) =e¹-1-t+(-3e-1+2t+1)µ(t-1) =e¹-1+(-2e¹-¹+t+1)µ(t-1)

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A: The given function is  f(x) = x5-x+2x3+7

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A: (a)

Q: Let f(x) = x7 Then f'(x) is 5æ5 + 3x³ – 3æ – 4. За — - - f'(3) is f' '(x) is and f''(3) is

A:

Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

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A:

Q: dx J x (In² x – 6 ln x + 10)

A: SOLUTION-

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A: Given query is to find the derivative of the function.

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A: Given: f ( x ) = - ( x3 + 2 x ) ex+2          To Find: f' ( x )

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A: Let fx & gx be two differentiable functions. The product rule of differentiation is given by:…

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A: By using differentiation property, we calculate the required value.

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A: We are given : X(s)=s2+6s+7s2+3s+2 ⇒X(s)=s2+3s+2+3s+5s2+3s+2 ⇒X(s)=1+3s+5s2+3s+2 ---(1) Now,…

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A: The given function is

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A:

Q: Suppose f(-4)= -7 and f'(-4)= 7. Find t d (7x² + 10x + 3) f(x) at x = -4 is dx d f(x) dx 7x² + 10x…

A:

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A:

Q: Let h(t) = 3t3.2 7t-3.2 %3D | Then h'(t) is h'(1) is s! (7),.4 and h''(1) is

A:

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A:

Q: Suppose y(t) = c1 e^(-t) [1 -1] c2 e^(t) [ 1 1], with the initial condition y(1) = [0 2]. Find c1…

A:

Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

A:

Q: Differentiate. f(x) = (3x - 5) (Vx +4) O A. f'(x) = 4.5x'/2 - 2.5x-1/2 + 12 1/2 - 1/2 O B. f'(x) =…

A:

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Q: Substitute the value of y' in 1 + (y)²

A:

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A:

Q: (1) Let A={1,{2},{1,{2}}} (a)True or false: 2 € A, {2} € A, {{2}}CA, {1,2}CA, 3x(x € A^xA)

A:

Q: Let 7(t) = Find 7'(t) F'(t) =

A: The objective is to find the derivative of given

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A: We have given yt=y0·ekt·1-tp,  y0=p10 By dividing both sides of the equation by y(0), yty0=ekt·1-tp…

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