If a function f(x) is given by x²-2x-8 T²-7x+12' 6, is f(x) continuous at x = 4? = x 4, x = 4, Yes because lim f(x) = f(4). x 4 O2 No because lim f(x) does not exist. 3. No because f(x) is not defined at x = 4. No because lim f(x) exists, but lim f(x) = f(4). 2-4 x-4

Q: 1. If f(r) = , do the following: %3D iii) What is lim

A: Given Function, f(x)=1x

Q: x, x 2. y=h(x) 4 3 y-2 Show that a. lim h(x) + 4 b. lim h(x) + 3 c. lim h(x) + 2 X-2

A: Given, h(x)=x3,  x<23,  x=2  2,   x>2 now show the limit on x→2…

Q: Use the given graph of the function f to find the following limits: 1. lim f(x) = -I←x 2. lim f(x) =…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: 1 lim (3x¹ + x³ - 2x) lim (-x² +5x+6) 2 *→ lim √2x² - 8x-3 3 x→→ lim √x³ - 5x 4 x→ -

A:

Q: Let f(x) be a function with all of the following properties. Sketch a graph of y = f(x). Explain…

A: given that the function f(x) is a function with the following properties: a) f(-1)=2, f(1)=1 and…

Q: , if x + -1 -2, if x = -1 Prove that f(x) = {x+1 is continuous at a = -1 by showing the following.…

A:

Q: lim g (y) where, g (y) = = y² +5 3-3y lim 9 (y) y² +5 ify < -2 -9 lim g(y) 3-3y if y≥-2 y-2 ify <-2…

A:

Q: 3. Use the graph of f(x) below to answer the following questions. a. lim f(x) b. lim f(x) x-1 c. lim…

A: The given graph is: Use the graph of f(x) to answer the following: a. limx→1+f(x)b.…

Q: lim g (y) where, g (y) = = Jy²+5 3-3y lim g(y) y² +5 if y -2 ify <-2 if y≥-2 g(y) --1 = -1.9 √y²+5…

A: We can draw the graph of the function and interpret the limit  of the function.

Q: If V5 – 2x? < f(x) < V5 – x? for -1 <x < 1, find lim,-o f(x).

A: Given  5-2x2 ≤ f(x) ≤ 5-x2 for  -1≤x≤1.

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: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: lim g (y) where, g (y) = Jy²+5 3-3y lim g (y) y² +5 ify < -2 -9 lim g (y) 3-3y if y2-2 ify <-2 if…

A: Given :limx→-2gy where gy=y2+5if y &lt;-23-3yif y≥-2

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: lim g(y) where, g (y) = [y²+5 13-3y lim g(y) y² +5 ify < -2 y+ 2 lim g(y) 3-3y if y≥-2 ify <-2 if…

A: First we have: gy=y2+5      if y&lt;-23-3y     if y≥-2 Now, limy→-2 gy=limy→-2y2+5=9          if…

Q: 31. If f is continuous and f(3) = 9, which of the following statements must be true? (A) lim f(3x) =…

A: Here we define which statement is true or false.

Q: Given the graph of y = f(x), 1 -1 True False y -2 then x2 y = f(x) lim_ƒ (x) = 1 2 3 X

A:

Q: Let f be a function with continuous f" such that f(3) = 0, f'(3) = 2, and f"(3) = –1. Evaluate the…

A: use L Hospital Rule to find the given limit.

Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

A:

Q: 3. Sketch a graph of a function (x) for w ich all of the fo lowing are true: lim-2' f(x) = -4,…

A:

Q: = lim g (y) where, g (y): +-2 y²+5 3-3y lim g(y) y² +5 ify < -2 -9 lim g(y) 3-3y if y ≥-2 ify <-2 if…

A: Part (1):-  Given function is gy = y2+5    if y&lt;-23-3y   if y≥-2

Q: lim g (y) where, g (y) = y² +5 3-3y lim g (y) y² +5 ify < -2 -9 lim g (y) 3-3y if y2-2 if y<-2 if…

A: Follow the procedure given below.

Q: Let F (x) = { tan (x − 3) x < 3 x-5 3 ≤ x Then lim F(x): x 3- = CH M₂ 146

A:

Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: 7. Explain why for any function g, limg(c +h) = lim g(x). Use this to show that f'(c) = lim f(x) –…

A: Consider the given function limh→0gc+h=limx→cgx

Q: x²-49 X-7x²-7x 2. Evaluate lim: 3. Evaluate lim √x+1-3 X-8 x-8

A:

Q: lim g(y) where, g (y) = Jy²+5 13-3y lim g (y) y² +5 ify -2 ify <-2 if y2-2 9 (3) = -1.9 DNE y²+5 if…

A: The given function is a piecewise function represented as: g(y)=y2+5   if y&lt;-23-3y   if y≥-2

Q: -2 -2 y²+5 if 9(y) = {1-3y if --1 -1.04 DNE (a) lim g (2 3-6 (b) lim g lim g (y) y² +5 y+-2 lim g(y)…

A:

Q: Enter each answer as a whole number (like -4, 0, or 253) or D

A: Given,