If f is continuous from the right of x1 and lim f (x) exists, then lim f'(x) = f'_ (x1). O True False

Q: Find the limit limx→π/2(sinx)tanx.

A: We use tan(x)=sin(x)/cos(x)

Q: How many times must l'hôpital's rule be applied to evaluate ex - e-X – 2x lim X + 0 X- sinx

A:

Q: Use the limit definition of the derivative of the given function at the given value of x (if it…

A: Given functions are

Q: What is the limit of (sinx)/x if x approaches to 0?

A: Given: A function limx→0sin xx and x approaches to 0. Since sin xx is an intermediate form of type…

Q: 4. Show that In x lim x→1 x – 1 1. (Hint: Note that In In x-ln 1 x-1 and interpret the limit as a…

A: Given: To prove that limx→1 ln xx-1=1 using the limit as a derivativeFormula:…

Q: Find limit   \lim _{x \rightarrow \infty} \sin x/ x

A: A limit refers to the value that a function approaches as the input approaches some value.…

Q: Rearrange lim x* so that we can apply L'hopital's rule. *→0+

A: Follow the steps.

Q: Fill in the blank/s:

A: A function f(x) is said to be continuous at a point x = a, in its domain if the following three…

Q: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: Use the limit definihon of the that gex)= derivative to show 9(x)= 3 3 has denvahre X+5

A:

Q: 1. Find the derivative of f(x) = 2. at x = 0 using the definition of the derivative as a limit. Va +…

A:

Q: limit as x----0 for the function (px)/(sqrt(bx+a^2))-a using L'Hopitals

A: Apply the limit.

Q: Compute the derivative of h(x) = 3x – 5 using the limit definition (do not use L'hopital's rule).

A:

Q: Find the derivative of f(x) = √x^2 + 1 at a = 2, using the limit definition (i.e. first principles)

A:

Q: Express the limit as a definite integral on the given interval. n X;* -Дх, [1, 9] lim (x;*)² + 4 n-…

A: limn→∞∑i=1nxi*xi*2+4∆x,    1, 9 Here, fx=xx2+4, a, b=1, 9

Q: Find the derivative of g(x)= (x+1)/(x+2) using th limit definition.

A:

Q: Evaluate limit as x approaches 0 from the right of (1+x)cotx

A: Given, limit expression

Q: (4) Find the limit by interpretting the limit as as an appropriate derivative. (DO NOT USE…

A:

Q: Express the limit as a definite integral on the given interval. lim -Дх, [1, 4] (x;")² + 9 i = 1 dx

A:

Q: State the definition of the derivative of a function f. Use the definition of the derivative to…

A:

Q: Find limit sinax lim x→0 sinbx

A:

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

A:

Q: Use L 'Hopital's Rule to find the limit:

A:

Q: 3. y = at point (0, -) X-3

A: Topic = Derivative

Q: Find the derivative of f(z) = at z= 0 using the definition of the derivative as a limit. Be sure to…

A:

Q: b): By using L'Hopital rule to evaluate the limit tan x - sin ac lim 23 sin x

A: We need to find limit.

Q: 2+x2 lim X→0 X-2

A: The given limit is: limx→∞2+x2x-2 To evaluate this limit, take the x common on both the numerator…

Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

A:

Q: Evaluate the limit. (If an answer does not exist, enter DNE.) y= lim (10x)$sin(7x) X0+ %3= Work must…

A: Now we will find the value of the given limit.  We know,   sinx = 1/ cosecx

Q: 2х Use the Limit to determine the derivative of f (x) Then X-1 check your result by using the…

A:

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

A:

Q: 6. ) Express the limit as a derivative and evaluate. x2021 - 1 lim x - 1

A: we have to solve the limit problem

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: How many times do you have to apply L'Hopital's rule to evaluate the limit x- sinx lim x+0 x²

A:

Q: 3) Use the limit definition of the derivative to find f' (x) if f(x) = - %3D

A:

Q: Find limit   without using derivative

A: Given,

Q: lim X+x cos x sin x cos x 1-

A: We will split the numerator into two parts and try to get a general form of limit. Remember : As x…

Q: 1) Use the limit definition to find the derivative of the function f(x) = 6x – x². Then find all…

A: Using limits definition:f'(x) = limh→0 f(x+h) - f(x)hf(x) = 6x - x2f(x+h) = 6(x+h)- (x+h)2   = 6x +…

Q: Evaluate the limit. (Enter your In(x) lim *1 sin(5Tx)

A:

Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: Find the derivative of f(x) = 1/√(x + 1) at x = 0 using the definition of the derivative as a limit.…

A:

Q: lim x→0 for sin(4x)/3x

A:

Q: Is f continuous at x = 1?

A: The condition of continues function is, limx→a+fa=limx→a-fa=fa   For limit of function from the…

Q: 2. Evaluate the limit by Use the definition of the derviative to compute the derivative of f(x) = 1…

A: Given,

Q: Let f(x) = ln x / sin^-1 x    analyze the limit : lim x--> 1- (from the left) f(x)

A: Given information:The given function is

Q: lim (x²Vx* – 1 – x*)

A:

Q: limx→1 (x − 1) tan(x³ − x) - (x+1) sin²(2x - 2)

A: limx→1(x-1)tan(x3-x)(x+1) sin2(2x-2)=limx→1tan(x3-x)(x+1)×(x-1)sin2(2x-2)using propertylimx→af(x).…