x + sin x x + 1 lim f(x) = 1 (you are allowed to assume that | sin x| ≤ 1 for real x). 818 Let f R\{-1} → R, f(x) = : = Prove directly from the definition than

Q: Consider the piecewise defined function Find the values of a and b that make the following function…

A:

Q: x° + x2 ) lim x-1 || x +1

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

Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x>0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: Re Prove directly from definition that it f is a positive function so that lim +(x)=16, then…

A:

Q: Without using a calculator, show that the following function cannot have more than 1 real root. f(x)…

A: See the attachment

Q: If f(x) = cos x + sin x, what is f"" (x)? 46 f""(x) = sinx- cos x f"" (x) = sin x + cos x o f(x) =…

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

Q: Example 2. Prove that lim f(r) =1 by use of Definition 3, where f is given by - 21 +2 if a 2 f(x) =…

A: Given the proof of limx→2fx=1, where fx=x2-2x+22if x≠22if x=2 Here equation (c) is, fx-1≤32x-2 Also,…

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: Let f(x) = x³ 3x - 1.5. Determine whether the Intermediate Value Theorem can be used to show that…

A:

Q: Consider the piece wise function – x² + 16 x 4 VI

A:

Q: x2-sin 3x A/ Write the Sandwich theorem and applying it to find lim x2+10 if -1< sin 3x <1

A:

Q: 1. Let f:R R be defined by {1 if x rational number, 12 if x irrational number f(x) = Show that f is…

A:

Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

A:

Q: lim F(x),

A:

Q: cos x and g(x) x²-x-6 a) What is f(x) g(x) b) What is the domain of f(x), g(x) c) Determine the…

A:

Q: f(x) = ln(x² - 2x − 35) + √√4225 – x² Use interval notation to indicate the interval of continuity…

A:

Q: 2. Consider f(x)=x² – 4x + 2 a) lim f(x) x-2 b) lim f(x) x-4 c) lim f(x) We X-1

A:

Q: I +b if x > 2 2) Suppose f(x) ={a if x = 2 if r < 2. (a) Find the value of b if lim f(x) exists. (b)…

A: Solution

Q: (a) Explain both mathematically and graphically what makes a function odd or even. b) Use the limit…

A: (a) Suppose fx is a function then mathematically it is said to be odd if  f-x=-fx And graphically, a…

Q: 16. f(x) = 3x2+36x+108 step 1 f(x + Ax): step 2 f(x + Ax) - f(x) f(x + Ax)-f(x) step 3 Ax f(x + Ax)-…

A: The differentiation of the a function can be obtained using the numerical differentiation. This can…

Q: If lim x→0 a) f(x) x = 1 and lim x-0 lim g(x) x→0 g(x) – 2, evaluate: X b) lim x-0 g(x) f(x)

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: tan(31x) lim x → 0 5x

A:

Q: Evaluate the function for values of x that approach 1 from the left and from the right. f(x) = x3 -…

A:

Q: The first and second derivatives of a function f are given. Use these to find the information below.…

A:

Q: 2). 8(x) = Now A is it is given function real numbers. Therefore it is at 4 = -1 x = 2. lim f(x) =…

A: Given function is fx = 4x ;  x≤-1ax+b ; -1&lt;x&lt;2-5x ;  x≥2 Also, given that function fx is…