Why is the following function discontinuous at x = 1? (1+x² ifz <1 f(x) = 4 - if x > 1 (a) f(1) does not exist. (b) lim f(x) does not exist (or is infinite). x→1 (c) Both (a) and (b). (d) f(1) and lim f(x) exist, they are not equal. x→1

Q: . Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

A:

Q: 8. Find the indicated limit 2X √x + 1] X lim(- X→∞0

A:

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

Q: Find the limits: Vx – 1 lim x→1 x - 1 а.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Verify the limits in a given equation below. (x+h)²-h² lim X→0

A: Verify itx→0lim(x+h)2-h2x

Q: Determine whether the shown statement makes sense or does not make sense, and explain your…

A: The functions whose graphs can be drawn without lifting the pencil off the paper is a continuous…

Q: For the function f(x)= e^x cos(x^2), find the equation of the tangent line to the graph of f(x) at…

A:

Q: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: If f(x) is differentiable at X =c then lim f(x) must exist and f(c) must be defined

A:

Q: 2. Write the equation of a function that is discontinuous at x=5, but lim f(x) exists, and is…

A:

Q: Prove rigorously that lim lxl = 0.x→ 0

A:

Q: x³ - 8x* +1x lim xa -5-14

A: Dear student our policy is to answer first one only in case of multiple question kindly repost the…

Q: 8. e 1 Build a table to estimate lim x+0 X

A:

Q: find the limit of g(x) as x approaches the indicated value.

A: limx→13x2+1gx=∞

Q: Evaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

A:

Q: Express the limit as a derivative.

A: To express: limit limx→-1x3+1x+1 as a derivative. Concept used: Definition of derivative:…

Q: If lim f"(x) = +00, then the trapezoid estimation Tn - f(x) dx O TRUE OFALSE can never be within…

A: Given,

Q: Suppose g(x)=4x^2-lnx is the derivative of f(x). Compute Lim x->0 (f(x+1)-f(1)/x) Please show steps…

A:

Q: Find the limit as x approaches - 2 for the function f(x) = 12x + 1. %3D lim (12x+1) = X→-2

A:

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: Ali is trying to find the limit of a function which is expressed as L = lim x→0+ (1 + x)1/x . From…

A:

Q: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

A:

Q: 2-メ Compite lim %3D Xラム z(T-X)

A:

Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

A:

Q: Find the limits limx→0+x-1/ln x

A:

Q: Find the indicated if it exists: lim x to +infinity;  2x2+3x+1 divided by x4 - x2

A:

Q: 2x-1 2. lim X-2 \3x+4,

A:

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

A:

Q: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

Q: Find the limit of lim((9+3x)1/2-3)/x as x approaches 0

A: To determine the value of the limit.

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: If lim f"(x) = +0o, then the trapezoid estimation Tn - | f(x) dx %3D x0* can never be within 10¯³ of…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

A:

Q: According to the alternate form of the definition of the derivative, to compute f′(0), we need to…

A:

Q: 1-√3-x 4. lim. x→2 4-x²

A:

Q: Q4) A) Find the following limits (for two only). x+1 1. lim x--1 x2-x-2 1-Vx 2. lim x-1 1-x 2x 3.…

A: 1. limx→-1 x+1x2-x-2   is of 00form, So apply L'Hospital rule limx→-1 x+1x2-x-2   =  limx→-1…

Q: find the lim as x approaches infinity when f(x)= (1-x)/2x

A:

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A:

Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

A:

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=f'(0)…

A:

Q: Let f(x)={−4x+3   x≠4               {3       x=4. What is f(4)? If f(4) does not exist, type: 99999…

A:

Q: if Væ² – 5x – 6 < f(x) – 1 < v6² – x² then find lim f (x) - | - x-6

A: Given:x2 - 5x -6  ≤ f(x) -1 ≤ 62 - x2To find : limx→6f(x)

Q: Find lim at inf: (x^2 + 2x)/(x - 7) Don't use L'H

A:

Q: (2) Suppose that a function f(x) is defined for all real values x except x* x,, then lim f(x) does…

A: For limit to be exist at a point, left hand side and right hand side values of function should be…

Q: + 34, find f '(x) using the definition f '(x) = lim h→0

A:

Q: + 1for all positive x-values, then what is lim f(x)? X+ 4

A:

Q: T is discontinuous at -1 because lim f(x) as x--> -1 does not exist. * %23 .7. 5. %23

A:

Q: . For a function f, suppose lim f(x) does not exist because values of f(x) oscillate between two…

A:

Q: Find g'(x) for g(x)=-x^2+3x+2 by using the limit definition of a derivative.  lim x-->0…

A: