cos(x), for x < 0 for x = 0 (1– x², for x> 0 9) Using the definition of continuity, explain why the beautiful piece-wise function f(x) =}1, is continuous at x=0. Show work to support your explanation (You will need one sided limits. Pointing to a graph is not good enough).

Q: Calculate the limit for the function f(x) = x +4 over the interval [0,4]. Verify your answer by…

A: The given function is : f(x)=3x2+4 on the interval 0,4 For geometrical interpretation, The graph of…

Q: The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a…

A: Given information:Tyhe given function is cosh(x).

Q: Find the limit: Lim x-->0  2 sin2 3x / 3x2

A: you know that:

Q: Calculate the limit for the function f(x) = x + 4 over the interval [0, 4]. Verify your answer by…

A:

Q: Use continuity to evaluate the limit. lim 4 sin(x + sin(x))

A:

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: (a) Evaluate lim (1+ sin x)xl. x→0- (b) Determine whether or not f(x) = (1 + sin x)XI is continuous…

A:

Q: Find the limits. Are the functions continuous at the point being approached?

A:

Q: Use continuity to evaluate the limit. lim 9 sin(x + sin(x))

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: Suppose that f (x) is known to be continuous, and the graph of ƒ (x) on [a, b] has no • corners •…

A: Problem is based on definition of continuity and differential

Q: Find the limit. lim x--> 0  sin x/2x-sin x

A:

Q: sin(x – 3) lim X→3 + 6x – 27

A:

Q: Calculate the limit for the function f(x) = Ex + 4 over the interval [0, 4]. Verify your answer by…

A: Given the function

Q: 1. Express the limit as a definite integral on the given interval. Xi lim Ax, [1, 3] '(x;)² +13 n00

A:

Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

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

A:

Q: Calculate the limit for the function f(x) = x + 4 over the interval [0, 4]. Verify your answer by…

A: We have to find the limit of the function f(x).

Q: 02.) Find the limit lim X+x cos X sin x cos x 1- X→0 lim sin 5x SIn 4x 3-

A:

Q: The slope of the tangent line to the graph of f(x) = tan(sin-'(x)) is not defined at x = 1. %3D…

A: Consider the function, Recall that the slope of the tangent line at any point of the curve is…

Q: Find the limit and determine if the function is continuous at the point being approached. (- lim sin…

A:

Q: limit of (x + 5) as x approaches to 3 po yung given if ever blurred. ty!

A:

Q: Find the limit. 2+5x+ sin x lim 3 cos X 2+ 5x + sin x lim | (Type an integer or a simplified…

A: To findlimx→ 02+5x+sinx3cosx

Q: Calculate the limit for the function f(x) = x + 4 over the interval [0, 4]. Verify your answer by…

A: To find the limits

Q: Express the limit as a definite integral on the given interval. lim Ax, [1, 4] (x;)2 + 3 dx Need…

A: Given query is to write the expression as integral.

Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

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

A:

Q: Find the limit as x-->0 of sin(-3x)/sin(2x)

A:

Q: The continuous extension of (sin x)^x [0,π] a) Graph f(x)= (sin x)^x on the interval 0 ≤ x ≤ π.…

A:

Q: Suppose f is continuous on the interval (0,3). Assume further that f(0)= -2 and f(-3)= 5. Also, lim…

A:

Q: True or false √2 If cosh x = V, then sinh x = 2. It is possible for a function to have an absolute…

A: To determine whether the following statements are True or False.1 If cosh x=62, then sinh x=22.2 It…

Q: What is the limit (as x approaches 0) of (sinx-tanx)/x^3?

A: lim sin x -tan xx3=lim sin x -sin xcos xx3=lim sin x cos x -sin xx3 cos x =lim (sin x x cos x)(cos x…

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Investigate limit x 0 sin(pie/x)

A: Here we need to find the following limit:

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: Express the limit as a definite integral on the given interval. lim -Ax, [1, 6] (x)2 + 5 n- 00 dx…

A:

Q: Calculate the limit for the function f(x) =x+4 over the interval [0, 4]. Verify your answer by using…

A: we have to find the limit for the function f(x)=32x+4 over the interval [0,4].  The formula used to…

Q: ind the limit. lim x→0  sin(3x)    7x

A: Consider the given expression: limx→0sin3x7x We know that, limx→0sinxx=1

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

A:

Q: Find the limits: (1) lim (tan x)* X-0+ (2) lim (sin x)* (3) lim (ex + x)² X-0+ X-00

A:

Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: Find the limits. Are the functions continuous at the point being approached?

A:

Q: Use l’Hôpital’s rule to find the limits

A:

Q: Find the limit (if it exists) and discuss the continuity of the function. If limit does not exist,…

A:

Q: Calculate the limit for the function f(x) : 13 x +4 over the interval [0, 4]. Verify your answer by…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 3. Show that the function | sin(2.x)| is not differentiable at r = 0 but the function | sin(2x)|1+T…

A:

Q: a function is continuous at x = c, then the limit exists as x approaches c. If the domain of a…

A: a. If a function is continuous at x = c, then the limit exists as x approaches c By the definition…

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.