97. Let f(x) = ax² + bx + c, where a, b, and e are odd integers. If x is an integer, show that f(x) must be an odd integer. [Hint: x is either an even integer or an odd integer.]

Q: 3. Let f(2)= and let C = {2 € C : |2| = 1}, described in the positive sense. Determine the value of…

A: 3. Given function as f(z)=z4-5z2 and C=z∈ℂ:z=1

Q: Suppose f(x) = 4nx2e Ax* for all x E R. Show that f = -f. %3D -e

A:

Q: 9.J. If F is a non-empty closed set in R and if x ¢ F, is there a unique point of F that is nearest…

A: As per BARTLEBY GUIDELINES, I answered one question (Q-9.J.) and repost other questions separately.…

Q: 2. Prove that a) the function f(x) = tan x+x can be replaced by g(x) =x if x→0. b) the function…

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Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

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Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

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Q: Let g(x) -x V25- x. A+ where (25 -je" A 9"(x) where (25 - x)"

A: As per our guidelines, we are allowed to answer only one question. Since, you have asked multiple…

Q: -2 is a critical number of the function f(x) = /2x – a %D - Select one: True False

A:

Q: Let f(x) = Vr - 5, g(x) = , h(a) = , Find go((gof)+h(x)) at x=-1? 2-9'

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Q: Let f(x) = – 5 In(7x) f'(x) =

A: Given,           fx=-5ln7x

Q: Let f(2) = In[="(= + 7)*(z² + 7)°] f'(x) =

A: Given : fx = lnx8x+72x2+76

Q: Prove that for x≠0 the inequality ex>1+x holds.

A:

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: Compute f'(a) for a = 3. f(x):

A:

Q: Let f(x) = (|x| + x2 − 1     if x ≤ 0          (|x| − x2 − 1     if x > 0 Is there some x in (−1, 1)…

A:

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−4x−3,g(x)=2x+2, and h(x)=4x^2+2x+2, what is k′(x)

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Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

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Q: 4. Use the definition of "f(x) is 0(g(x))" to show that 2* + 17 is O(3*).

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Q: 15. If f(x) = 3 – 9x³ + x, which of the following is true about the end behavior of f (x)? - As x →…

A: According to question given:f(x)=3-9x3+xWe have to calculate the end behavior of f(x).

Q: (a) Prove or disprove: f: Z3 → Zs, [r]3 + [r*]5 is well defined.

A:

Q: if ニ if 1-X fCx +2) = f(x) Hx f on [-3,3] and we Suppose draw the funch'on

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Q: (b) Suppose f'(x) > 1 for all x > 0, and f(0) = 0. Show that f(x) > x for all x> 0.

A: We will be using mean value theorem

Q: let foo- X-1 when x+i- Féndavalde of fethat calil makefis continueus at xe

A: For a function f(x) to be continuous at x = a the condition is:

Q: Find the domain of the function. h(x) = In x + In(2 - x)

A: Given h(x)=ln x+ln (2-x) Find the domain by finding where the expression is defined.

Q: Use the IVT to show that f (x) = x3 + x takes on the value 9 for some x in [1, 2].

A:

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: (х — т 11- тх if x < 3 if x 2 3 5) Find m so that g(x) = Is continuous for all x?

A:

Q: O f(x)=x2, when f: Z Z O f(x)=x?, when f: Z-z O f(x)-x2, when f: Z Z O f(x)=x2, when f: Z Z

A:

Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: 5. Show that if X~F.m, then X-1 ~Fm.,

A: The probability density function of a random variable X:It is given that the random variable X…

Q: If f(x) =x²-x over x-1 and g(x) =x is it true that f=g?

A:

Q: Which of the following correctly describes the end behavior of f(x) = -x* +2x ? O A. As X → - 0,…

A: Given:- Function f(x)=-x4+2x

Q: 2. If p and q are positive integers, f is a function defined for positive numbers and attains only…

A:

Q: If you are asked to find L4 for f(x) = edz) + In(x) on the interval [2,10], what would the value of…

A: From the given problem:   fx=e3x2+lnxa,b⇒2,10   As we know that the expression for the step size is:…

Q: 6 Evaluate f S Suh

A:

Q: 8. Decide if the following functions are onto. Prove your answers. (a) f(x) = x² – 1 (b) g(x) = 2x…

A:

Q: Compute f' (a) for a = 6. f(x) = 5/x

A:

Q: Let f(x) is defined as (kx² – 1, S (x) = x-1 Determine k so that the fur

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Q: 3 Prove that Var(aX– b) = a² Var(X) where a and b are constants. %3D |

A: We know that the V(X) =E(X2) -(E(X))2 By using the  above definition of V(X), we can easily prove…

Q: 2- Let f(x) = ()*O- , x = 0,1, is p.d.f then P(x = 0) =

A: The p.d.f.  of random variable X is: f(x)=13x231-x ;    x=0, 1

Q: a) Prove or disprove: f: Z3 → Z5, (r]3+ [r*]5 is well defined.

A:

Q: Determine the number c which satisfy the conclusion of Mean Value Theorem for f(x)=8x+e−3x on…

A:

Q: If the function f:R → R given by f(x) =x³+ax²+bx+5sin*is an increeasing function , Find the…

A: if F(x) is increasing function, then F'(x) must be greater than 0. So from that, we will solve this…

Q: Q. Let flx)- if x20 07 xt Prove that fX) = 2|X| for r every X X

A: Given function is,

Q: Let f(x) = x2/3. Show that there is no value of c in the interval f(8) – f(-1) 8 – (-1) (-1,8) for…

A: Given: The function, fx=x23.

Q: Find e so that f(x) is continuous on the entire number line. if x3

A: fx=x2    if  x≤3cx    if  x&gt;3 Since the given function is a polynomial function for all x&lt;3…

Q: 8.4 Let f=(x1,x2...,x,)E S,. Show that o(f)=r.

A:

Q: 5 + x, if -T <x<0 - x, if 0<x < A f (x) ||

A:

Q: 50. If f'(x) = In(x²) and f(5) = 8, then f(3) %3D %3D

A: Given : f'x = lnx2f5 = 8