dT -k(T - 35), where k is a positive constant. dt

Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: Express the equation in Heaviside Function

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Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: The acceleration a = the initial velocity v, and initial position of a body v(0) = 2, s(0) = −3.…

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Q: du = t2 + 3u, t> 0, u(5) = dt 100

A: Given differential equation tdudt=t2+3u and u5=100 ⇒tdudt−3u=t2⇒dudt−3tu=t2t⇒dudt−3tu=t Hence, the…

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: Final Examination The derivative of the function y = r + 9x at the point a = 4 is O 45 of 48 tion O…

A: We find derivative of y with respect to x I.e dy/dx = (d/dx)*f(x)

Q: 4x Let F be the function defined by F(x) = cos(t?) dt. Find an expression for 3. F'(x).

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Q: 4x Let F be the function defined by F(x) 1 dt. Find an expression for (t² – 5)6 F'(x).

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Q: r(a) e-t ta-1 dt

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Q: rsin x 3. F(x) = f* Vi dt %3D 3.

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Q: F(x) = 9t dt

A: given: Fx=∫0x29t dt Fx=∫0x29t dt=9∫0x2t dt=9t1+11+10x2=9t220x2=92t20x2=92x22-02=92x4-0=92x4

Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. X 21 d 1/² (316-1) ²¹…

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Q: 3sec2(t) Find f dt ? 6+3 tan (t)

A: Assume (6 + 3*tan(t)) = u and solve the integral.

Q: Let A(a) = |" f(t)dt where f is the function given by the graph below. 4- -2 -3 -4 А(5)

A: Consider  A(x)=∫4xf(t)dt

Q: t² - t dt 0, = (x)6 g'(4) =

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Q: Let G(x) = ²* w(t) - [² d dt. t4 a Find a function, w, and a number, a, such that G(x) = 4x¯ w(x) =…

A: Given G(x)=∫axw(t)t4dt and G(x)=4x-2-1

Q: L+ Ri = E,where L, R, and E are constants when t = 0,i = 0 dt %3D

A: We have to find the solution of  given first order linear differential equation

Q: Q10 x² +1 et dt. Find an equation of the tangent line to the curve off when Let f(x) = 3 + x². x=2.…

A: fx=3+x2∫5x2+1et2dt We have to find the tangent of the curve fx at x=2

Q: Find the derivative. d (2t-3) dt t+5

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Q: 9a) Find the local extrema of the function f(x) = e*(x² -3) using the Second Derivative Test.

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Q: Find: f 4t Vi + dt =

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