(a) Show that e>1+ x if x> 0. [Hint: Show that f(x) = e* – (1 + x) is increasing for x> 0.] (b) Deduce that s e**dx < e.

Q: Use Simpsons Rule to approximate e-x*dx using n = 8 and state a bound on the error. The fourth…

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Q: (a) y=e**' In(x² +2) 2+w? (b) f(w)=ln. w -2

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Q: Estimate n such that V * log(x) dx – T₁| < 10-8. Tn

A: for the function f(x)=logx  To find the value of n so that the error bound in trapezoidal and…

Q: Use the table below to find h'(2) for h (x) = g (f (x)). I(z) g(x) | S'(z) | g(x) 0. 1/2 1 -2 1 -3 1…

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Q: The graph of a function f is given. YA Estimate -1 0 te (10 f(x) dx using five subintervals with the…

A: We have been given the graph of the function f(x). We have to estimate ∫010fxdx using five…

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A: The random variable  follows a Poisson distribution with a parameter .Mathematically, .

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

A: Find the local extrema of the function f(x)=exx2-3. Using the second derivative test.  Determine if…

Q: Let f(n) = 100(2") and g(n) = n!. Prove that f = 0(g). %3D %3D

A: Given: f(n)=100 (2n) g(n)=n! To prove f=O(g)

Q: If f, g L₂ then [S* S(x)g (x) dx ] * ≤ [f*° ƒ^²(x)dx ] [1° g² (x) dx]

A: This is the famous Cauchy Schwarz inequality for integrals. It follows by working with quadratic…

Q: f (x) = e*²+2 at x = 1 with h = 0.5

A: As no method is mentioned, I am using Taylor polynomial of order 2 for approximation.

Q: -5x Integrate x² e

A: We have to find

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A: See solution below.

Q: 1.) lim In(4x) = 2.) lim In(x2 - 5) = %3D X→の 3.) lim In(x) = 4.) lim In(2x) = 5.) lim (-In x) = %3D

A: We have to find out the limit

Q: Which function has the characteristics below? (x) has an x-intercept at (2.0). As x approaches…

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Q: Q2 Let X,X, f(r;8) = e/",I > 0. (i) Show that f(x:0) is a member of the exponential class. (ii) Find…

A: X1, X2, ...., Xn is a random sample from f(x,θ). We first calculate the likelihood function. If it…

Q: Suppose f(x) = x² In(x). then f"(e) equals

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Q: x² -1 ,find f'(x) and f"(x). x? - 3x+2 If f(x)= 4. „find f"(0). x-1 If f(x)= e* 5,

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Q: Let {X} be i.i.d. such that X₁~ Pa(4, 1500) and suppose that N(2) ~ Po(100). Find E[S(4)] and…

A: Given that  be iid. such that  and

Q: The graph of f is given to the right. Let g(x) = f(t) dt. (a) Find g(3). (b) Find g'(-2). (c) Find…

A: Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: Find f (x). 1- e* f(x) = 7+ e f'(x) =D

A: Given query is to find the derivative of the given expression.

Q: 3 2x 11-8 n x³ + 1/ 5 where [ ] = G.I.F If lim /2n dx = k, find the value of [1] + 2013.,

A: Solution :

Q: Let f(x) be piecewise continuous and a -exponential. In this case, prove that F(s) L £{f(x)} = F(s)…

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Q: -- Let the function f(x) have the property that f' (x) = x+1 If g(x) = f(x²) find g' (x). х-5 g'(x)…

A: Simply use the chain rule of derivative .

Q: If ɛ ER and the function f(x) = ex – 1+ x² is increasing x E R, show also that e >

A: Since f is increasing hence f'(x) &gt;0 for all x