if x < 1 if x = 1 g(x) = 2 - x2 if 1 < x< 2 x - 3 if x > 2 valuate each of the following, if it exists. (If an answer does not exist, enter DNE.) lim g(x) x-1 ii) lim g(x) X→1 iii) g(1) iv) lim g(x) x→2 v) lim g(x) (vi) lim g(x) X2

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: If g(x) is differentiable at x = 1, then lim g(x) = g(1). x+ 1+ True False

A: A function f(x) is differentiable at x=a, if limit exist at x=a and is equal to f(a)

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: -3 -110 lim g(x) = x→2- lim g(x) →2+ = lim g(x) = = x→2

A:

Q: If 3x < f(x) < x³ + 2 for 0 < x < 2, find lim f(x). x-1

A:

Q: 5. Sketch the graph of one function y = f(x) that satisfies all of the requir- ments below. lim f(x)…

A:

Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

Q: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: -4+x, x)= {=-x if x 2 3 if x 3 Evaluate the following expressions. lim f(x) = x-3 lim f(x) = x-3+…

A: f(x)=-4+x,    if x&lt;3   2-x,    if x⩾3 now I am attaching image so that you can easily understand…

Q: f(2 + h) – f(2) Find lim if f(x) = x + 7. h h→0 f(2 + h) – f(2) lim | (Simplify your answer.) h h→0

A: Here I am attaching image so that you understand each and every step.

Q: If lim f(x) = 15 and lim g(x) = 25 then x5 x5 lim 3f(x)g(x) –- 6] = x5

A: Given that limx→5 fx =15  and limx→5 gx=25 find limx→5 3fxgx-6=?

Q: Find lim f(x) if f (x) = 3Vx + 2 x 2 %3D X-2 Determine the intervals where the function given in…

A: Given f(x=3x+2x&lt;2x2+2x≥2

Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

A:

Q: If  lim x→1  (f(x) − 8)/(x-1)=2     , evaluate  lim x→1 f(x).

A: Given: limx→1f(x)-8x-1=2

Q: 52. Let X if x 2 (a) Evaluate each of the following, if it exists. (i) lim g(x) (ii) lim g(x) x→1…

A: Limit exist at x = a If left hand limit = right hand limit lim x→a- g(x) = lim x→a+ g(x)

Q: If lim f(x) = 16 and lim g(x) = 24 then x8 lim[3f(x)g(x) – 7] = O 1159 O 1152 O 1145 O 216 O 32

A:

Q: Consider the graph of y=f (x) 5 3 C -5 -4 -3 -2 -1 10 11 -1 Which of the following is true? (A X--3…

A:

Q: Let g(x) and h(X) be functions with lim g (x) = G and lim h (x) = Hwhere G and H are real numbers.…

A:

Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

A:

Q: If 5-4x sf(x)s5-x for - 1<xs1, find lim f(x), lim f(x)%= f(x) =D

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Q: Suppose f(x) and g(x) have the following values: • f(8)= -4 and f'(8)= -6, g(8) 1 and g'(8) = -3. =…

A:

Q: if x1 then lim,-1 f(x) is 3 if x 1 (b) 3 3. Let f(x) = (a) 1 (c) not exist (d) other

A:

Q: If lim f(x) = 11 and lim g(x) = 26 then x→6 lim[3f(x)g(x) – 6] x→6

A: We first distribute the limit…