The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits x² + x – 1\/3 lim &r2 – 3 x-00

Q: x² + kx – 10 Find the value of k that would make the lim exist. lim X – 2

A: Explanation of the answer is as follows

Q: Determine if the following piecewise-defined function is differentiable at the origin. 4x - 6x° - 1,…

A: topic - derivatives

Q: 4.) x²-9 lim X-3 x-3

A:

Q: Evaluate the limit: x² +6x+8 ]im as x – – > - 4 lim x-4 x+2x-8 2 x ^ 2+ 6x + 8 divided by x ^ 2+ 2x…

A:

Q: find the limit of rational function (a) as x→0 and (b) as x→ -0. x³ + 7x? – 2 g(x) x² – x + 1

A: Given  g(x)=x3+7x2-2x2-x+1

Q: find the limit of rational function (a) as x→00 and (b) as x→ -o. 3x7 + 5x? – 1 f(x) 6x3 7x + 3 -

A: (a) Given f(x)=3x7+5x2-16x3-7x+3 For x→∞…

Q: For the function f(x) given below, where x > 0, evaluate lim f(x). X18 f(x) = ln(9x³ + 10) - In(2x²…

A:

Q: Determine whether f(x) approaches ∞ or –∞ as x approaches 9 from the left and from the right. 1 f(x)…

A:

Q: Determine whether f(x) approaches o or -o as x approaches 5 from the left and from the right. -1…

A: fx=-1x-52=limx→5--1x-52=limh→0-15-h-52=limh→0-1h2=-∞

Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: The given limit expression is limx→ -∞ 1-x3x2+7x5.

Q: (x +1) 2)(x +2)(x (x + 3)(x+ 1)

A: Let,  f(x)=x-2x+2x+1x+3x+1

Q: Evaluate lim f(x) and lim f(x) for the rational function. Then give the horizontal asymptote off (if…

A:

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 5x8 – 2x3 + 9 h(x) 3 + x – 4x5

A: [a]limx→∞5x8−2x3+9−4x5+x+3 Therefore, limx→∞5x8−2x3+9−4x5+x+3=∞

Q: Evaluate lim f(x) and lim f(x) for the following rational function. Use co or - o where appropriate.…

A:

Q: Determine the limit by sketching an appropriate graph. for x <4 S-3x - 4 8) lim f(x), where f(x) = {…

A:

Q: • For the graph of the piecewise function f(x) shown below, determine the values of the left- sided,…

A:

Q: find the limit of rational function (a) as x→00 and (b) as x→ -o. 9x4 + x 2x4 + 5x² – x + 6 h(x)

A: Given h(x)=9x4+x2x4+5x2-x+6 a) To find limit of h(x) as x→∞ limx→∞h(x)=limx→∞9x4+x2x4+5x2-x+6…

Q: Given the function f(x)= 5+x; x4 a)On which interval(s) is the function continuous? b)Circle the…

A: a) A function is said to be continuous if  Left hand limit = Right hand limit = f(a) Left-hand limit…

Q: Given the following piecewise function, 2x2+3x-5 f(x) = x 0 1. Identify and classify points of…

A:

Q: Given the piece-wise function x² – 2x + 5, Зx2 — 2х —5 f(x) = 0 2 Find lim f(x) and lim f(x) x-2…

A:

Q: For f(x) = the square root of 7x+30, how can I find f’(x) using the definition f’(x) = lim as h—>0…

A: Given,          The function is fx=7x+30.We know that,          The derivative of the function is fx…

Q: 2x-5+4x² lim 3-5x+x²

A: To find: The limit of limx→∞2x-5+4x23-5x+x2. Given: The limit is limx→∞2x-5+4x23-5x+x2. Formula…

Q: 1. Under which circumstances for an infinite limit could you ONLY state mf(X)= DNE and not say that…

A: 3. Consider a function: fx=x2,x&lt;2……1x-2,x≥2……2

Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: To find the limit  limx→-∞4-3x3x6+9

Q: 1. For the function ƒ whose graph is given, determine the following limits. 3 lim f(x) X2 -6 -5 -4…

A: A limit of a function at a point exists if at that point the left-handed and right-handed limit…

Q: Given , 3x + 2 f(x) = x - 2 (i) Carikan asimptot mendatar. Find its horizontal asymptotes. Зx+2 Зx+2…

A: We will use rule for calculating asymptotes of a function

Q: What is the value if a so that f(x) has a slant asymptote of y = x + 3. x²+ax+5 What is the limit of…

A: Given: fx=x2+ax+5x+1 We know that slant asymptote is possible when the degree of the polynomial in…

Q: Find the following limits if they exist. Must show all work (analytically?): 1. lim f(x) where f(x)…

A: We will find out the limit of given function.

Q: lim 2 x²-9 2 x² - 4x +3 where c = 0 and 1

A:

Q: 2. Find the horizontal asymptotes for the following functions, using limits. x²+2x+1 а. f(x) 4x2+x+5

A: Using definition of horizontal asymptote ,

Q: Determine if the following piecewise-defined function is differentiable at the origin. 7x- 2x - 12,…

A:

Q: find the lim as x approaches infinity where

A:

Q: For f(x) = (-x^3+1) / (2x+8), evaluate limx→∞ f(x) and limx→−∞ f(x). Then give the horizontal…

A:

Q: definition showing all work for credit b.Write the equation of the tangent line to the curve above

A: Derivative: f(x)=7x-4x2 a)       h→0limf(x+h)-f(x)h=h→0lim7(x+h)-4(x+h)2-7x+4x2h

Q: 5. Given that -3.x2 + 9x – 5 < f(x) < x² – 3x + 4. Find lim,→-3/2 f (x). x2 + 6x + 9 For what values…

A:

Q: x- 9 lim x-9 x²- 81 2.

A: Topic   = Limits

Q: Given f(x) = 2x^2 + x -15 all divided by x+3 find lim x -> -3^f(x) algebraically is f(x) continous…

A:

Q: X-9 lim

A:

Q: lyfical of the itemrs need to be factored or rationalied for the limits to exist) - 1. lim (x - 2r)…

A: given,        3.  limx→-4x+42x2-164.  limx→-33x2+2x-1x2+3x+2

Q: We are given the following. 8x2 - 9 lim 9x? + x - 3 We note that as x becomes large, both the…

A: The solution is given below.

Q: If 8x – 19 < f(x) < x² + 4x – 15 determine lim f(x) x→2 What theorem did you use to arrive at your…

A:

Q: 1. Without a table of values and without graphing f(x), give the values of the following limits and…

A:

Q: Determine whether f(x) approaches o or -0o as x approaches 9 from the left and from the right. -1…

A:

Q: -x2 if x 3 Iff (x)

A: Take value of f(x) for value of x just less than zero.

Q: Find the limits below x³ – 3x + 2 (a) lim x2 – x t3 – 3t + 2 (b) lim t-1 t2 – 2

A:

Q: Find the limit of the rational function a. as x→x∞ and b. as x→-. x2 + 11 f(x) = 3 x° + 15 2 + 11 a.…

A: a)

Q: lim (3x2 – 5x + 9) X-4

A: Given query is to find the limit of the expression.

Q: What type of discontinuity is at x = 3, if lim f (x)= 0 and lim f (x)= 0? x-3 x>3* What type of…

A:

Q: Evaluate lim f(x) and lim f(x) for the rational function. Then give the horizontal asymptote of f…

A: