3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b) O C= [3] ³ and c = [3]²³ c) c = 1 d) O There is no c that satisfies the theorem. N/W

Q: Describe all the numbers that are in the domain of f(t) V4+ 6t 3 Ot 2 2 Ot 0 Ot2 - 2 3 3. Ot < 2 Ot…

A: Function and it's domain

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

A:

Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: Which of the following is not equal to P(100, 2)? 2P100 100! 98! 9900 100P2

A: We have given, P(100,2) The number of permutations of n things taken r at a time is defined as,…

Q: How many zeros does the function below have 1 31 - g(1) + Vi +1- 3.1, (-1,1) O A) 4 O B) 3 C) 0 O D)…

A: Given:

Q: e the exact value of the function for the given x-value without using a calculator. ( ) f(x) = f(x)…

A:

Q: )(2n) for conplex number sequance show that if lm En=1 then 3no fN such that for for Hn 7 no o Znto.…

A:

Q: Supposer FCE, acE is algebraic F and dog (a/F) 13 odd. Proveo that F(a)= F(a²). over

A:

Q: Using the Mean Value Theorem, prove that √1 + x² 0. Make sure to check all the necessary conditions…

A:

Q: The Range of y = [2x + 1] is Z, T O F

A:

Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

A:

Q: Consider the interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

A:

Q: 5. If x is an integer, then x' 2x. b d a C 6. There exists a real number x such that x'= x . FL

A: we can solve this problem using some basic properties of integers and real number.

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval. У(х) %3D…

A:

Q: Use the Mean value Theorem to prove that 1/9 ≤ √66 - 8 ≤ 1/8

A: Use the Mean value Theorem to prove that

Q: 31. Letf(x) = [x²/3]. Find f(S) if a) S = (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: 31. Given the function is                            f(x)=x23.

Q: Let X ∼ N ( 1 , 4 ) and Y ∼ N ( 2 , 9 )be independent and let W = X2 +2Y + 3. Then what is the mean…

A: Given, Therefore,

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: Show dz 4 In= 는I미페 - for a<0. x <

A:

Q: 1. State the properties of the Bassel function.

A: Here are some properties of Bassels Function

Q: 2.11. Show your steps. a) Find all integers x such that 4x =11 9. b) Find all integers z such that…

A:

Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

A:

Q: Verify Mean Value Theorem for the function 3x? - 4x +5 in [-1,1]

A:

Q: 1. Let a and b be real numbers such that a < b. Apply the Mean Value Theorem to f(x) = In(cosh x) to…

A:

Q: Use the mean value theorem to show that |sin a – sin b| < |a real values of a and b where a + b

A: let f(x)= sin x f is continuous  on [a,b] and differentiable  on (a,b) Therefore there exist  c such…

Q: f(x) = 3x - 2sınx +7 %3D aluse the intermediate Value Theore m to show that flx) has at least one…

A:

Q: Use the Mean Value Theorem from §4.2 to prove that | sin(b) – sin(a)| < 16 – a| for any interval [a,…

A: