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)

Q: x - x +2 4. If flx) =x + 7 find f'(x) . (5x - 1) (3x²) (A) (x' + 7)(5x - 1) – (x° – x + 2)(3x²) (B)…

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

Q: +(n) = 3 (²³-9x² +33m - 18 enfor 1) Ⓒincreasing in (-0,0) (Ⓒineressing M- L decreasing in (2,8) in…

A: The function is given by:-Since, the natural log is present in the function.Domain of the function…

Q: Calculate s'(n) (8n + 5 s(n) = 2n-6/ 6

A: The given function is s(n)=8n+52n-66 To find the s'(n). Derivative formula:…

Q: 1 •[₁ F(X) -1 Given f(x) dx = 0 and (a) [f f(x) and [₁ f(x) dx. 1 (c) [₁² (d) (b) • [² f(x) dx - [°…

A: (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.

Q: -1² ƒ'(x) = 3x² √√x6 +1 If f(x) = √t² + 1 dt then

A:

Q: dx J x (In² x – 6 ln x + 10)

A: SOLUTION-

Q: What is t' (x) if t(x) = Select the correct answer below: = 80x5 .? ex O t'(x) O t'(x) = 80( -). ○…

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

Q: f(x) = (-x³ – 2x)e*+2 f'(x) =?

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

Q: fy (x² Inx)*, then dy dx Select one: a. 4(xPInx) (x+ xInx) b. 4(x3+Inx) (2x+ C. 4x (Inx) (1+2lnx) O…

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

Q: Find B so that B^2 = A where A = 1 -1 0 -1 2 -1 0 -1 1

A:

Q: X(s)=(s^2+6s+7)/(s^2+3s+2) and Re{s}>-1 what is x(t)?

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,…

Q: If f(x) = x cosh then f'(9) = 1 ¹() x²-9

A: The given function is

Q: -1 Find L s2–18s+40 s(s²–6s+10) |

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:

Q: Determine the chromatic numbers of the wheel graphs W₁, n ≥ 4. Justify your answer.

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:

Q: What is r' (x) when r(x) = In (x³ + 2x2 + 3x +1)? Select the correct answer below: In (3z2 + 4z + 3)…

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: List all intervals for which there are possible unique solutions (t-5)x''-ln(t)y'-y=et

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:

Q: for g(t)=t^4-t/2t+5 find dg/dt { t=2

A: Given the function is g(t)=t4-t2t+5 To find dgdt  at  t=2

Q: I got to the step where I have (5h/h-1)/h. I think I can multimply (5h/h-1) by (h/1). This results…

A: We have to find actual expression for the given expression.

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

A:

Q: x) [in(3x²-36)]². Then f'(x) = A. 12x In (3x²-36) 3x²-36 O A. O B. O C. O D. O E. 2 In (3x²-36)…

A:

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

A: The objective is to find the derivative of given

Q: Solve for k:  y(t) = y(0) * e^(kt* (1-t/p) )  (we know that y(0)=P/10)

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…

Q: A small company of science writers found that its rate of profit (in thousands of dollars) after t…

A:

Q: -8x Since f'(x) then (x2 - 4)2' (x? – 4)>(D) - (-8x)[2cx? – 4)(Ox)] _ 8 x2 f"(x) (x2 (y2

A:

Q: L-1 { 10 / (S-2)(S2+1) }

A: Let  As-2+Bs+Cs2+1 = 10(s-2)(s2+1)A(s2+1)+(Bs+C)(s-2)(s-2)(s2+1) = 10(s-2)(s2+1)A(s2+1)+(Bs+C)(s-2)…