How many functions exist with the signature Za → Zb?

Q: 1 is th -1] f'a', for w

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Q: Find f'(x). f(x) = In x 44 + X f'(x) = (Type an exact answer.)

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Q: 14. Show that if f is a monotone function defined on [a, b] that satisfies the intermediate value…

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Q: Compute P(0), and find the exact values of the six circular functions given that 0 = – 135°.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Show that if f: A-> B is continuous and A is compavt then f(A) is also compact

A: Let , f : A →B be continuous function. Here , A is compact set. We need to prove that , f(A) is also…

Q: The domain of the function h(t) = vt – 9 is O [9, 00) O R O (-00,9) O (9, 00) O (-∞0,9]|

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Q: Suppose h is a function such that h(3) = - 2, h'(3) = 2, h'"(3) = 3, h(5) = 5, h'(5) = 7, h''(5) =…

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Q: if f:[0,2] 3 R such that if x>0 f(x) = { ²2 if x<0 show that whether f is continuous in [0,2]

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Q: Which of the following decomp inside function) is/are correct ?

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Q: Let F be the collection of all functions f: N-→ {0,1}. Is F countable ?

A: A set S  is countable if there exists a one-to-one map from the set to the set of all-natural…

Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

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Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: Suppose and z are functions of x and y, then prove.

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Q: The domain of the function g(t) = vt – 8 is O (8, 00) O [8, 0) O (-∞, –8) O R O R-{8}

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Q: D. Prove that f(x) = |x - 6| is continuous at all points c in R.

A: Given function is fx=x−6. We have to prove that the function fx=x−6 is continuous at all point c in…

Q: Suppose h is a function such that h(3) = -2, h'(3) = 2, h"(3) = 4, h(5) = 6, h'(5) = 7, h"(5) = 13,…

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Q: Describe the long run behavior of f(z) = z" As z + - 00, f(z) - As z + 0, f(z) → ( -0-

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Q: A on S is a function from S×S into S.

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Q: Find the Green function of L[x] = x" on [–1, 1].

A: As per the question we have to find the Green Function of the operator L , defined as : L[x(t)] =…

Q: Define Euler's P-function. Showing your working, compute (5), D(23) and (115).

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Q: Let f(æ) = In(z') f'(2) =

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Q: Suppose h is a function such that h(2) = -2, h'(2) = 2, h"(2) = 4, h(5) = 5, h'(5) = 7, h"(5) = 12,…

A: We have to solve

Q: Suppose we have a function k(t) such that k(7) = 10 and k' (7) = –0.25. %3D

A: b) Assume k(t) = At2 + Bt + C

Q: Find the first 3 iterates of the function f (x) = 0.75x when 0 = 5. O 5, 3.75, 2.8125 O 3.75,…

A: To get the next iterate, apply the function f(x) to the previous  one.

Q: 2. Find the first 3 iterates of the function f(x) = 0.75x when xo = 5. %3D 5, 3.75, 2.8125 4.25,…

A: First iteration is x1 = .75*5 = 3.75... Second iteration is x2 = .75*3.75 = 2.8125... Third…

Q: Determine if g (r)= is continuous at a = 8.

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Q: What is the total change of f(x), if ƒ'(x) = 2x − 3x², over the interval [0, 3 -18 -12 -6

A: Given query is to find the total change for the given intererval.

Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]

Q: Is defined for some value of s?

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Q: prove the reduction formula for the bessel function .

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Q: The function on ℤ defined by f(x)=-x^2-5 is onto. True or False ?

A: The given function is                  f(x) =x2-5   Graph:

Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

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Q: Compute P(0), and find the exact values of the six circular functions given that 0 - 135°. = -

A: θ=-135° Now x-coordinate of Pθ is, cos-135°=cos135°   ∵cos-x=cosx=cos180°-45°=-cos45°…

Q: 5. Find all analytic functions f such that Ref + Im f = ry.

A: We need to find the analytic functions f such that Re f+Im f=xy. Consider the function of the form…

Q: Show that f (a) = is Libschitz function on r+ 2

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Q: Find a function f ( x) such that 5+ f(t) -dt = 4/x for and some number a а.

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Q: Define a function g(x) of a random 1; if x2x, 0; otherwise variables by g(x) = %3D Where x, is a…

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Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: Let x be a continuous

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Q: Suppose that f(x) is continuous and differentiable, f(2) = -2, f(6) = -6, and f(x)dx =-10. Compute ,…

A: Topic:- Functions

Q: Suppose h is a function such that h(1) = -2, h'(1) = 2, h"(1) = 3, h(2) = 6, h'(2) = 5, h"(2) = 13,…

A: Given: The second derivative is continuous everywhere.

Q: Determine f, (x); f (x) = In(x² + x)

A: The given function is                      fx=lnx2+x We want to find fx(x), that means partial…

Q: a) Suppose that f(x) = 4x if x<-1 = cx + d if – 1<x< 2 = -5x if x 2 2 Find values of c and d such…

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Q: A function f :N Z which is one-to-one and onto.

A: Suppose we have a function . Condition of f is one-one . Suppose such that , then . Condition…

Q: øz (@) is a continuous function of o in the range -o < @< ∞.

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Q: Consider f(x)= In (1+x ). With the chain rule, one

A: SOLUTION-

Q: if |f] is in L^1(A), then his in L^1(A)?

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Q: Express the following functions in the form u+iv f (z) = In(z)

A: The complex number: z=x+iy can be written as z=reiθ, where r=x2+y2 and θ=tan-1yx. Using the…

Q: 5. Find all analytic functions f such that Ref + Im f = xy.

A: To find all analytic functions f such that Re f + Im f=xy.

Q: (4) Are all entire functions bounded on D?

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.