2. Here, ƒ is the function given by f(x) = Find the limit, if it exists lim x→2 = arcsin (#) f(x) − f(2) x-2

Q: tan 3x lim x→0 \ e2x – 1 3/2 O 1/2 O 2 O 2/3

A: Solution:GivenTo find the limit oflimx→0 tan 3xe2x-1=?Formula:ddxeax=aeaxddx tan ax=asec2 ax

Q: f(x) – f(c) If lim exists, it equals the slope of the х — с to the graph of f at the point (c,…

A: If    limx→cf(x)-f(c)x-c  exists;

Q: Let f(x) = x² + 3x – 2 f(x) – f(1) a) Find lim x- 1 x+ 1 b) Use your answer in part (a) to find an…

A:

Q: (2) Use the definition of limit of a function to find lim x³-3x-2 x+2x2 - 3x+2

A: To find the limit of the function x3−3x−2x2−3x+2 as x approaches 2, it can apply the definition of…

Q: 6. Is it true that the limit of a function lim f(c) = L is the same as evaluating a function f(c)?

A: the limit of a function lim f(c) = L is the same as evaluating a function f(c)

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: (6x+3y)sin(2x+ y) lim (x,y)→(0,0) 4x² +4.xy+ y

A:

Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

Q: Compute the derivative of f(a) the limit definitions. rf from the limit definition. Note: you can…

A: The given function is:fx=x23

Q: Express the limit as a derivative.

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

Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

Q: Use the graphs of f and g and their tangent lines at (-1,0) to find f(x) lim Number x-1 g(x) y f(x)…

A:

Q: f(r+h)-f(x) 1. Use the definition f (x) = lim to find the first derivative for the function h0 h…

A:

Q: In (2-x) 1-x²-y2¹ (a). Find and sketch the domain of f. 1. Given function f(x, y) = ,do the…

A:

Q: limit of a function f(x) as x approaches c is always equal to f(x). True or false

A:

Q: Draw a graph of a function that satisfies the following p 1) f(x) 0 for x>0 3) f(0) = 0 %3D 4) f is…

A: Given description of function 1) f(x)<0 for x<0 2) f(x)>0 for x>0 3) f(0)=0 4) f is…

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: Use the limit definition of the derivative to determine f '(2) if gnibnoqonos su snimals (T ni 4 =…

A:

Q: For the piecewise linear function, find the following. (If an answer does not exist, enter DNE.)…

A: NOTE: Refresh your page if you can't see any equations. . the given piece-wise function is

Q: 2) a) Recall that the definition of the derivative of a function f at a point a is given by f(a + h)…

A:

Q: The equation for the line tangent to f (x) at the point (7, 11) is given by y = 12x – 9. Use f(7+h)…

A: The equation of the line tangent is given by y=12x-9 Let ''m'' be the slope of tangent.…

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: Consider the function H(x): = 23 + 2x - 1 10x + 2 if x > 3 if x < 3 Determine if H is differentiable…

A: