Answer all the following questions 1. Find the domain of f(x) =x-4 x-4 2.Solve the inequality and show its solution sets on the real line 5 3-Evaluate the Limit lim 5x – 2x2 +1 1- 3x 4-If. 2-x < f(x) < 2Cos(x) for all x then find: lim f(x)

Q: х2 — 2х-15 x2 — х— 20

A: We have to evaluate the following limit: limit as x tends to 5, [(x2 - 2x - 15)/(x2 - x - 20)]

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: Find the limits x2 – 4x + 8 lim I -00 3x

A: Given  We need to find the limit.

Q: 3. Find lim x-2 x - √5x + 6 x-6

A: The limit is given by limx→2x-5x+6x-6 To evaluate: The value of the limit.

Q: Find the limitsof: lim 34 メ+34 -V34 メしe

A:

Q: Analyze the discontinuities of the following piecewise-defined function. Include a well-labeled…

A:

Q: (x3 - 3x2 +6- 2x) 10. Use a table to estimate lim X-+3 X- 3

A: Given limx→3 x3-3x2+6-2xx-3-1

Q: x2 + 8x + 15 if x 2. Find lim f(x). x-2+

A:

Q: Consider the following graph of the function g. From the given graph of g, state the numbers at…

A: The graph of a function g is given, to find its points of discontinuity.

Q: Find the limits x* + x lim Xo 12x + 128

A: The limit gives the value towards which an expression converges as its variable approach to certain…

Q: Find the length of the graph of f(x) - + 1 1≤ x ≤4

A:

Q: Find the limits 3x lim x→-5 2x + 10

A: Our Aim is to find the limit of the expression given below:-limx→-5- 3x2x+10-(i)

Q: 10 a. lim 3-2 2x+1 b. lim Z x-3

A: Given 1.      lim x→3 10x-22.       lim x→2 2x-1x-3 To find - the value of the given limits

Q: Find the limit L. 2x2 + 8x + 6 lim X--3 x + 3 L =

A: Factorise 2x2+8x+6 2x2+8x+6=2x2+6x+2x+6                     =2x(x+3)+2(x+3)…

Q: A function is said to have a vertical asymptote wherever the limit on the left or right (or both) is…

A: Key points: 1. lim x→2-fx =  limh→0f2-h   (Left hand limit)2. lim x→2+fx =  limh→0f2+h   (Right hand…

Q: Evaluate the limit 9-x lim x 9 3-√√x

A:

Q: r2 + 8r + 15 if r<2 if z 2. if a <2 Let = f(x) 4x +7 lim f(x). I-2+ Find

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.