Prove the properties C at 0 h { eªt f(t)} = FCS-a) @h{f} = sh{f}-fee) (3 @ h { p²n} = sn h{f} - 5" - (0)-5-²P (0)... [²4 (10) R. r in lov? VA (-1)^_Inf

Q: c. - f'(1) = (3e³ – 2p¹³) In (5p¯² — *√p) -

A: To differentiate the given expression f′(1)=3e3−2p−1/3ln(5p−2−p−1/4), we'll need to apply the chain…

Q: Suppose f"(x) = - (sin(x)), ƒ'(0) = –2, and f(0) = -3. %3D Find f(1/4).

A: Given,          Suppose f''x=-sinx , f'0=-2 and f0=-3.

Q: solve

A: We have to choose the correct answer from the give

Q: .3 Find the derivative of the function f(s)= 12s³+ 5secs. a. f'(s)=36s² + 5secs · tans b. f'(s)= 3s²…

A: We have to find derivative

Q: Does g(t)=3t^5+10t^4−30t^3+70 have any inflection​ points? If​ so, identify them. An inflection…

A: The given function is: g(t)=3t5+10t4-30t3+70 And, the derivatives are:…

Q: Find f'(x) and f"(x). f'(x) f"(x) = f(x) = (x³ + 7)ex

A:

Q: By writing T/4 = (T/3) - (T/4) and considering e^iT/12, evaluate cot(T/12) and tan(T/12).   Where T…

A:

Q: Apply Richardson’s Extrapolation on the centered-difference formula: f'(x0)=2h[f(x0+h)−f(x0−h)]−…

A: …

Q: 15- Consider the table below. If f'(x)g(x)dx= 5 then what is the value of f(x) 2 f'() 6 -3 g(x) -4 3…

A: Given  ∫01f'xgxdx=5 and x 0 1 f(x) 2 4 f'(x) 6 -3 g(x) -4 3 g'(x) 2 -1

Q: If f(w) = w-3 In w + arcsin w, find f'(w).

A:

Q: TLP iadade mnts & smt Findf F'(t) =sec(t) (seclE)+ tan (ED), -st < f- FCt) = -<ts f (--7 2.

A: We simplify f'(t) by expanding  To find f(t) we integrate f'(t) C=integrating constant

Q: y = f(r) Refer to the graph of y = f(z) above. If f" (2) exists everywhere, which of the following…

A: Derivative

Q: Find f' (7. 50) from the following table : 7. 48 · 195 7. 47 7. 49 7. 50 7.51 7. 52 7. 53 y=f (x):…

A:

Q: 3) Find the total derivative for each the following cases: a) Find dy/dx: y = 4x2 + 2x², where ==…

A:

Q: Suppose f" is continuous everywhere. For any constants a and b, show that xf" (x) dx = bf" (b) –…

A: Explained below

Q: 0.6z Express the function h(x) = Ve' - 3 in the form h(x) = (ƒ o g)(x) where f(x) # x and g(x) ± x…

A:

Q: 8.. If L' { f(p)} = F (t) then L1 {f( ap) } is : a) aF(at) b) F (t/a) c) F(at) d) (1/a)F (t/a)

A:

Q: Si f"(t) = f (t) e² = e4t + 2t¹/4, ƒ'(0) = 2 et ƒ(0) = 3, alors =

A:

Q: Find the Upper Bound (UB) and Lower Bound (LB) for f (x) = x' – 3x +24. a. Unbounded. b. LB =-3;UB =…

A: The lower bound of a function is obtained if the polynomial is divided by x-c using the synthetic…

Q: Find the intervals where h(x)=x'+24r-168r2 is concave up and concave down. Σ BIU

A:

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: (c) Trapezoidal rule with end corrections using the first derivative and third derivatives (a) a

A: Consider the given integral. I=∫-11e-x2dx Now, find the derivatives up to a third of the function.…

Q: Let r(t) = (- Find 7' (t) r' (t) = ( (..) -5 - 2t -3t+3' 5t² - 4 - 3t² -6³-5

A:

Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

A:

Q: Q1 (a) Let X1,..., Xn be iid obser vations from an exponential(A) pdf, where A has the conjugate…

A: Im bayesian probability theory if the posterior distribution p(θ|x) are in the same family as the…

Q: 1) di If f(x+k) dx=8, where k is constant, then -1 k+3 Shfl k-1 f(x) dx=?

A:

Q: Q1 find f'(x) using (forward finite difference formula ) at x = ½ for f(x) = sin x - e* with h= 0.1,…

A: Sol

Q: The derivative of the function Ve-tanh a is O y = -sech3x vetanh z 2 O y = -sech?x Ve-tanh / 2 O y =…

A:

Q: 31) Find the shaded Area A between two curves ftop(x) = 6 – x2 and gbot(x) = 2, over [0, 2] as shown…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dn Find a general formula for den by identifying a pattern in parts (a) through (c). To begin,…

A: We use the given details and differentiation formula to find answer

Q: Find the value of f(-1) when ƒ"(t) = 6(2t − 1) and ƒ'(1) = 6, ƒ(1) = 1.

A:

Q: 1. What is true about the function f(x) = b* ? (Circle ALL that apply) c. f'(0) = Inb b + 1 b. x>0…

A: Find your answer below

Q: 6. If f(w) = arctan w + 4", find f'(w).

A: