sin x 13. Using the definition, determine whether the function f(x) = , x #0 is continuous at x = 0. 1 x = 0 Justify the conclusion.

Q: Evaluate the following limits.

A:

Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x² + 2x + 1…

A: Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: O Find the values of a and b to make the function ffx) is continuous everywhere sin ax if x < 0 f(x)…

A:

Q: Find constants a and b so that each of the following limits is true. Va + bx а. lim 1 = 2 b. lim tan…

A:

Q: Evaluate the following limits. x + sin(x) + 2vT x + sin(x) V1+x – 1 – 5 a) lim 2 b) lim r2

A: Given: a  limx→∞x+sinx+2xx+sinxb limx→01+x-1-x2x2

Q: find limit that represents the slope of the tangent line to the following function at x = 2 ? 2 f(x)…

A: Given function f(x)=24-3x To Find that represents the slope of the tangent line to the following at…

Q: Suppose that f(x) is a differentiable function such that f'(8)=7 and f(8)=1. If g(x)=cos(f(x)), then…

A:

Q: Choose the correct answer for the following limit S sin t3 dt lim 3x4 (A) (8) -1 (C) 1 4 (D) 4. (E)…

A: Let us consider the function F(x)=∫a(x)b(x) g(t) dt Then the derivative of the function is given by…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: Given: Function f(x) = 3x - cosx  To Find The x - values for which the given function is not…

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

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A:

Q: sint 1 COs t 13. lim t+0 t t

A:

Q: 1. For f (x) defined below, at what values is f discontinuous? if x < 0 (sin x, 1, if x = 0 f (x) =…

A: Solution

Q: O:: A- Find the limit for the following functions: - tan2x 4x-3 3x3-9x²+x-3 1- lim x→0 sin4x 2- lim…

A: A) Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Consider two functions f(x),g(x) defined for all real numbers. Let the two functions be continuous…

Q: Is the following function continuous F(x)=x cot 5x

A:

Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: 1. Use the definitions of the hyperbolic function to find each of the following limits. sinh(x) lim…

A:

Q: Suppose that f(x) is a differentiable function such that f'(8)=7 and f(8)=1. If g(x)=cos(f(x)), then…

A:

Q: (a) By using L’Hôpital's rule, evaluate each of the following limits. sin x lim x-0 2x (i) (ii) lim…

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: Evaluate the limits of the following functions, and verify your answer. (6x+3y)sin(2x+y) 4x? + 4xy +…

A:

Q: Find the following limits. Do not apply L'Hospital's rule. ペ-4 lim +2 |x– 2| (i) (ii) sin (3t) lim

A:

Q: 2 If x sin x = So f(t) dt, where f is a continuous function, find f(0). (Hint: remember that the…

A:

Q: Choose the correct answer for the following limit S sin t3 dt lim 2 x4 (A) (B) (C) 1 8. (D) 4 (E) -4…

A: Given,

Q: C-The result of the following limit is sin t² lim 1-0

A:

Q: S. The limit of the following function is: sin 2x lim X2x + x b) 0 c) 2 d) 1 e) None of the given…

A:

Q: 3. Given х— А ; х>1 f(x) = { 26+x – 3 3B ; x<1 Assume that f is continuous at x = 1. Find the value…

A:

Q: Choose the correct answer for the following limit So sin t3 dt lim 2 x4 (A) (B) (C) 8. (D) (E) (F)

A:

Q: (iv) Evaluate each of the following limits without using L'Hôpital's Rule. tant (a) lim t0 t + sin t…

A:

Q: We can now evaluate this limit to conclude that the derivative is as follows. 1 a1/3 + a2/3) f '(a)…

A: We have to evaluate limit

Q: Which of the following limits can be evaluated without l’Hôpital’s Rule? Evaluate each limit. sin x…

A: Compute the limit limx→0 sin xx3+2x+1 as follows. limx→0 sin xx3+2x+1=sin 00+0+1=01=0

Q: Find the constants "a" and "b" so that the following function (sin 2x, if 0<xs. sin 2x, if 0 < x < f…

A:

Q: Evaluate the​ limit, where a and b are constants with b≠0. lim x -0 sin ax/ sin bx

A:

Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 7 lim %3D х — 6 х—6 It…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Consider: f(x)=tanx4, −1&lt;x&lt;1x,              x≥1x,              x≤−1  tanx4is continuous on…

Q: t 1. lim t40 sin t t 2. lim t40 et - 1 sin(2t) 3. lim 2t t40

A:

Q: If f (x) is a function that is differentiable at x = 2 , then f (x) is continuous at x = 2. True O…

A:

Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 8 lim x→2 x - 2 = -4 It…

A: Consider the given expression limx→2fx+8x-2=-4 Or, -4=limx→2fx+8x-2                            …1…

Q: Consider the following function and answer the following questions. sin x f(x) = [-5,5] by [-5,5],…

A:

Q: Evaluate the following limits. x + sin(x) +2Vã x + sin(x) a) lim

A: NOTE***As per bartleby guidelines for more than one question, only first to be answered send other…

Q: 1) Find the following limits. Do not apply L'Hospital's rule. r² + x – 6 lim 1+2 r? – 2.r (a) (b…

A: (a).  We have to find:  limx→2 x2+x-6x2-2x

Q: 4. Use the limit definition of the derivative to test whether the following function f(x), given by…

A:

Q: ind the values of a and b to make the function f(x) is continuous everywhere sin ax if x <0 f(x) = {…

A: Given function is f(x)=sinaxx, x&lt;0x-1x2-1+b , 0≤x&lt;1x+1, x≥1…

Q: Evaluate the limits for each of the following; sin 3t lim 0 t(t +9) (a) sin? t lim t→0 3t2 (b) (x+1)…

A: limx→0sinxx =1 As you have asked multiple question we will answer only the first three subparts for…

Q: Choose the correct answer for the following limit S sin t3 dt lim X→0 2 x4 (A) 1

A:

Q: Decide if the function below is continuous or not using the three conditions of continuity. { x*sin…

A:

Q: Graph the function and observe where it is discontinuous. f(x, y) = e1/(x - y) fis discontinuous at…

A:

Q: ´ 1/x? sin x lim x>0

A:

Q: For f(x)=sin⁡x/2cos⁡x−1, at what values in the interval [−π,π] is f discontinuous?

A:

Q: Evaluate each of the following limits: (Show the complete solution. Do not use L'Hospital's Rule…

A: Here I am attaching image so that you understand each and every step.