Show that e* ≤ 1/(1 − x) when x < 1. [Hint: Consider f(x) = (1 − x)e*.] -

Q: s] B1(a): Find the value of k that makes function continuous at x = 4 x > 4 6x – k x < 4 3x + 6 f(x)…

A: The given function is fx=3x+6if x&gt;46x-kif x≤4. Assume that the above function is continuous at…

Q: 4. h(x) = x-T at X %3D 2. 5h(X) = x + x4-1 at X = %3D

A: Continuous function at x=a

Q: Suppose that ƒ′(x)&lt;= 1 for 1&lt;= x&lt;= 4. Show that ƒ(4) - ƒ(1)&lt;=3.

A: Show that:

Q: Suppose that a continuous function g satisfies: | 9(2)de = 12 and | 9(20)da = 24. Find og(3x²)dx.

A: Given that, ∫03gxdx=12, ∫06g2xdx=24 Let  ∫06g2xdx=24 Apply the substitution u = 2x to find this…

Q: 4-1. Suppose that f(x)= e¯ for 0< x. Determine the following: (a) P(1<X) (c) P(X=3) (f) x such that…

A:

Q: 95. Use algebra, limit rules, and the continuity of e* to prove that every exponential function of…

A: Given, f(x)=Abx To prove that it is continuous everywhere like ex

Q: Use mathematical induction to prove the following statement derivatives of the function f(x) = x¯¹…

A: We have to prove that the nth derivative of  where  is using mathematical induction

Q: 2. Suppose that f(x) = e * for 0< x. a. Determine x such that P(x < X) = 0.40 b. Determine x such…

A: Given:

Q: Write the functions in a list so that whenever f(x) comes before g(x), ƒ = o(g) or f = 0(g).…

A: The given functions are  ex, xx, lnxx, ex2, 2x, x2, ln2x. We know that f=og iff limx→∞fxgx=0 and…

Q: 10. Consider the following function. 1 x } x > Find the values of a and b that make f(x)…

A:

Q: Let 1, if-3 <x s2 f(x) = %3D 4-x, if 2 < x<4 Without graphing, is f(x) continuous at x 2? Clearly…

A:

Q: Q1 Let X1,. , X, f(r;8) = ()0"(1 – 8)²-²,x = 0, 1, 2. (i) Show that f(x;0) is a member of the…

A: It is an important part of statistics . It is widely used .

Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

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Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

A:

Q: 87. Suppose that f and g are continuous functions such that, for all a, := | g(x)dx Give an…

A:

Q: Use the e- 8 property in Definition 19.1 to show that f(x) 1 is uniformly continuous on the interval…

A:

Q: (153) (b) Let g(x) = 2***. Find g (x).

A:

Q: Show that for all x E (0, 00) we have In(x) <x – 1. Also, graph the functions In(x) and a - 1…

A: Suppose f is differentiable on an interval where I can be  . Note the result corresponding to…

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: . Let f(x) = (x² − 3)ex. Find all intervals where f'(x) is positive and all intervals where it is…

A: Please see the below picture for detailed solution.

Q: 1. Determine and completely simplify f(x + h) – f(x) for f(x) = -7 Зх + 1

A:

Q: Suppose that you know 3 18 O f(x) > 18 O f (8) – f (2) < 30 O f(1) is continuous on (-o, 00)

A: Using mean value theorem

Q: 4. Show that the function log(1+ x) lies between functions x - and x for all x > 0. (Hint 2(1+ x)…

A: We will expand log(1+x) by Maclaurin's series. Let f(x) = log(1+x)

Q: (b) Find parameters a and b such that the function jodonivi COS X f(x) = if if if x≤ 0 0 3 ax + b x²…

A: Given :

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: Sketch a graph of the function f that is continuous on (-∞,∞) and has the following properties.…

A: