Problem 5: Using the above result, show that if f(t) = tn, then n! (L{f})(s) sn+1> where n! = n(n – 1)(n – 2). . - 2 ·1. (Hint: write f(t) =t - t"-1 so that you get (L{t"})(s) in terms of the n-th derivative of the Laplace transform of 1.)

Q: (5) Use the limit definition of derivative to prove the following: (a) For any a e R, (f(ax))' =…

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Q: Find the derivative of y with respect to x 3tan-1x + sin-1x = 4

A:

Q: Find the derivative of the following function. (3x² – 5) y = Cos z + (x² + 1)0* sin 5x

A: Given  y = 3x2-55sin5x + x2+1cosx

Q: Use the "First Principles/Limit" to find the derivative of the function S(t) = t2 – t, at t = -1/2

A: Given  S(t)=t2-t To find the derivative using first principle at t=1/2

Q: 15. Evaluate the derivative. [(2t – 3) (1 + 1)] O -4t + 1 O -41 O 4t – 1 O 41

A:

Q: 3 - 1 Find the derivative of y = - 3 with respect tox. tan A. 3 x +9 В. + 9 С. 1 x +9 D. x² +9 B.

A: Use given function find derivative

Q: Find the derivatives of the following functions. Do not simplify your answer! d x2 + 3 (a) dx Vax +…

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Q: 10. Use the chain rule and the fundamental theorem of calculus to compute the derivative of the…

A: Liebniz rule for differentiation under integral sign:Let…

Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 4. Find the derivative of the following function by first expanding the expression. g(r) = (6r³ + 9r…

A: Use L'Hospital rule.

Q: (b) A poll commissioned by a politician estimates that t days after he makes a statement denegrating…

A: We have, S(t) = 75(t2-3t+25)(t2+3t+25).  i) Here, we have to find the derivative of S(t), i.e.,…

Q: 2. During the class, we derived in detail the first order Richardson extrapolated derivative, by…

A: Given Data: Dh1 ≡f'(x0)-h4/480 f(5)(x0) + O(h6) let during class, we derive in detail the first…

Q: Find the derivative of (a) f(z) = (z+4 sin z) (1-7 cos z), and %3D sin z (b) g(z)

A: Part (a) Given function is fx=x+4sinx1-7cosx

Q: 7. Let f(x) = (x² + 7x) e. Calculate f"(1), the sec- ond derivative of f at x = 1. (a) 2e (b) 17e…

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Q: 7 + Vx + x dx

A:

Q: Not yet answered Marked out of 6.00 P Flag question (A) Find the derivative of 13 1 y = t3 + 1 (B)…

A: y = (t^3 - 1)/(t^3 + 1)  derivative,

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.