Suppose f is a one-to one function with domain A and range B, then the domain of the function f1 is a) A b) в c) AnB d) None of these إختر أحد الخيارات (a) (b) (d)

Q: Show that f(2) =

A: We will show that derivative does not exist using definition. Then we will use geometry.  Calculate…

Q: Find the domain of the function. f(x) = /17-x O xIx 17), or (-*, 17) U (17, ») O xx 17}, or (17, ) O…

A: We have to find the domain of the function: fx=17-x We know for any square root function y=fx it…

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: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

A:

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x2 + 4 defined over the interval [-6, 6]. Justify…

A: Rolle's theorem is satisfied if : f(x) is continous at given interval. f(x) is differentiable at…

Q: Determine the function f satisfying both the conditions f'(=) = sec ( 5 ) tan (5) (4) tan (3) f(플)…

A: Given: f'(x)=secx3 tanx3 ;           such that  fπ2=4

Q: Explain the Wronskian of 2 functions f and g ?

A: Let f and g are the two functions. The Wronskian of the n functions is the determinant of the matrix…

Q: y = Sen4x

A: True explanation is given below

Q: let f: R-->R be given by f(x)= 3x^2 a. Show that f is NOT one-to-one b. is f onto? Explain

A:

Q: If PEZ explain why the function flx)=xP does not hane a Mäclausin Sevies -Formal a eleur explanetren…

A: To show, if p∉Z then the function fx=xp does not have McLaurin's series.

Q: There is an entire function whose value on the positive real axis is etR dt. Select de: O True O…

A:

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

A:

Q: 1, Use the definition of error function, prove that (주)나

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Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: Find the length of f(r) = on the interval [1, 2]. Show all calculations. %3D

A:

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: Let f and g represent differentiable functions such that f ″ ≠ 0 and g″ ≠ 0.

A: Concavity of a function can be determined using the second derivative of the function. If the second…

Q: Show that the functions are continuous on their natural domains with examples?

A:

Q: Determine two unique values of θ in the interval [0,2π), such that                    sec (θ) = 2√3/…

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Q: fスノ= 4ーズ, 〇Find!- U show thet f has Domoin f ? on inverse funyo -1 f ca) ?

A: The given function is  f(x) = 4 - x2 And x>=0

Q: IF Function F is bounded on [a,6], does F has as abs ,max and abs. min not ? or

A: We have a example such that that is bounded but not attains either absolute maximum or minimum.

Q: Prove that the function has a horizont

A: Please refer the attached image for complete solution. THANK YOU.

Q: If f(x) is continous on [a,b] then f(x) is differnitable on (a,b). True or False?

A: False Any differentiable function must be continuous at every point in its domain. The converse does…

Q: let F= Mit Ni + Pk

A: Given: Let  F→=Mi∧+Nj∧+Pk∧

Q: Let f(x) = Vx. Compute the difference quotient for f at a = 7 with h = 4. %3D %3D

A:

Q: Assume that f(x) = 5x + 2 and f is defined on [-1,5). Then f has an absolute maximum value at 5.…

A: In given problem since function f (x) = 5x+2 is defined only on [-1,5) i.e. 5 is not in the domain…

Q: prove using the IVT. √2 exists. Hint: Consider f (x) = x2.

A: we have to show √2 exists. Now let

Q: Find three relation from {1, 2} to {6, 7} that are NOT functions.

A: Solution is given below:

Q: Show that ( if f is decreasing is riemann)

A:

Q: Let f(æ) = In(z') f'(2) =

A:

Q: PROVE THAT Q(-∞) =1 usign Q – Function

A: Given that Q-∞=1

Q: Find four relations from {a,b} to {x,y} that are not functions from (a,b} to x, y}

A: We have to find four relations from {a, b} to {x, y} that are not functions from {a, b} to {x, y}.…

Q: If f is continous on[0,1] then f has an absolute maximum on (0,1)   True or false?

A: We will do it by a counter example.

Q: Find the left- and right-hand limits of the function fin Figure at x = 0, 2, 4. State whether f is…

A: Given-  To Find- The left- and right-hand limits of the function from the given Figure at x=0,x=2…

Q: Find four relations from {a, b} to {x, y} that are not functions from {a, b} to {x, y}.

A: It is given that the two sets are {a, b} and {x, y}. It is known that if A and B are the sets then…

Q: what valu e shouled be assigneed to a to make the function fex)= %3D 2ax

A: For the function to be continuous, the necessary condition is LHL=RHL=f(3) Here,  LHL=limx→3-f(x)…

Q: Let f be a function of multiplicity 5 at P. Then at P, µ(x) f(x) has multiplicity: f(x)'

A:

Q: Prove the interval [0, infinity) is closed but not bounded

A: Consider the provided question, We have to prove that the interval [0, ∞) is closed but not bounded.…

Q: If n= any integer, show that the function f(z) +[- z] has %3D removable discontinuity at x-n, here…

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Q: Let f(æ) = Vr² – 5, g(x) = , h(x) = go((gof)+h(x)) at x=-1? Find - %3D 22-9

A:

Q: Differentiate the function.

A: Given function -f(u) = lnu1+ln(2u)Differentiating with respect to u - f'(u) = ddulnu1+ln2uf'(u) =…

Q: If f is increasing on the interval [a, b), then f' does exist. Select one: a. True b. False

A: Let f is increasing on the interval [a, b]. Since, there is not given that the function is…

Q: Suppose f(x) is a continuous on the interval [a,b] and c is a number in (a,b). If f"(c) is…

A: If f(c) is a local maximum then f''(c) < 0 and if f(c) is a local minimum then f''(c) > 0

Q: Show that the function g(x)  =x| x has an inflection pointat (0, 0) but g"(0) does not exist

A: Given: The function g(x)= x |x| For x<0, |x|=-x, thus g(x)=x(-x)=-x2 Also for x≥0, |x|=x, thus…

Q: If f is continous on [0,1) ,then f has absolute minimum on(0,1) True or false?

A: Extreme value theorem says that, if a function is continous on a closed interval [b, a] , then it…

Q: prove two Function invezse each other fk)= (x-2)

A:

Q: Let f(x) dr = -8, f(z) dr = 3, g(x) dr = 7, g(1) dr = - = -15,

A: Given∫02f(x)dx=-8, ∫03f(x)dx=3, ∫02g(x)dx=7, ∫23g(x)dx=-15

Q: Find four relations from {a,b} to {x,y} that are not functions from {a,b} to {x,y}.

A: Given: Let A=a, b and B=x, y To Find: Four relations from A to B that are not functions.

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

A: