x2 - 9 The following problems concern the behavior of the rational function f(x) = (x +2)(x +3)(x- 4)2 near roots of the denominator.

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: If f(x)=2-3x². O a. O b. O c. lim h→0 lim h→0 lim 30 From first principles select the correct step.…

A: Given :fx=2-3x2

Q: Given that lim f(x) = -1, lim g(x) = - 3, and lim h(x) = 4, find X 2 x2 lim [f(x) • h(x)] g(x) f(x)…

A: limx→2f(x)=-1, limx→2 g(x)=-3, limx→2 h(x)=4

Q: Apply the properties of limits to solve the following problems: 1. lim (f(x) – g(x)) = x--3 2. lim…

A:

Q: 1. Consider the function fx3x+2, -x-6, x>0x<0. Use table of values to find the limit of the…

A: The given function,  f(x)=x+2,x&gt;0-x-6,x&lt;0

Q: 7. Find the limit of the following. a. lim(2x² - 4x + 7) b. lim X-5 X-4 x+2x -Sz-2x+4 c. lim x2 x-4…

A:

Q: 1) Consider the graph of f(x) given below and compute the limits: 15- 10 5 -2 -5 -10 -15 a. Lim f(x)…

A:

Q: lim V3x² – 6 X-2

A: The given problem is,           limx→23x2-6 Here the function is continuous and defined at x=2, so…

Q: Evaluate the following limits: x? – 4 - lim x→-2 x2 + 9x + 14 x2 – 4 lim x→-0 x2 + 9x + 14 V3x2 – 72…

A:

Q: Consider the graph of y = f(x). 4- -8 -7 -6 -5 -4 -3 -2 -1O 2 3 5 -2 For infinite limits, use 00 = 0…

A: As per our guidelines we are supposed to answer only first three parts. kindly repost others part as…

Q: Calculate the following limits. t2 - 2t - 3 lim t43 (t-3)3 a) |x-5| b) lim x+5- x2-4x -5

A:

Q: 1. Given that lim f(x) = 4 lim g(x) = -2 lim h(x) = 0 x→2 %3D %3D x2 メ→2 find the limits that exist.…

A: First note the properties of Limits of functions:   If fx and gx are two functions and if…

Q: Use numerical or graphical evidence to determine the left and right hand limits of the fund |32 -…

A:

Q: 1. Evaluate the limit for the graph lim f (x). x→1" f(x) 51 4- 3 2 1- -3 -2 -1 1 2 3 4 -1 а. 1 c.…

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

Q: 6. Evaluate the following limits analytically. a. lim 1-4 3x+1 r'- 5x - 6 b. lim 1-6 x - 36 c. lim -…

A:

Q: Problem 2.7 Let Find the limit lim f(x). x 0 f(x) = x² if x is rational 0 if x is irrational.

A:

Q: 1.5 Find the limit of the function, lim(x³ + 5x² – 7x + 1). x-2

A: Given,           limx→2x3+5x2-7x+1

Q: Find the limits of the Function 2 (x + h)² – x² lim h→0 h

A: We can solve this using the L'Hospital rule. And also from expanding equation we can solve easily.

Q: (2) Find the limit of the following: (a) lim 47 x2 -4 (c) lim x-1 1-x (b) lim (3x+11) X-4 x2 - 2x-63…

A:

Q: Calculate the value of the following limits algebraically, (if they 2x-1 a) lim x+1 X² 2x²-9x-5 b)…

A: Topic:- application of calculus

Q: Question 1 Evaluate the following limits: lim x-3 (x³+4x-13) lim x →-6 lim x²-36 x+6 2x² + 3x³ - 2x²…

A: Use l hospital rule

Q: 4. Determine the limits: a) b) 4x²-8xy lim (x,y)-(2,1) (x²-xy-2y², lim (x,y) → (0,0)…

A:

Q: We consider the rational function f(x) = p(x)/ q(x) = 2x ^2 + cx − 4c / x^2 − x − 2 . Here c is an…

A:

Q: Given lim f(x) = 7 and lim g(z) = - 3, evaluate: %3D lim (2f(x) + 4g(æ)) : lim (2 + 4f(x)) =| %3D (…

A:

Q: Use the graph to evaluate the limit. 3) lim f(x) x-0 3) 3+ 2+ 4 X 4) lim f(x) x-0 4) 3+ 10 -4 -3 -2

A: Graph of the function is given, we have to find its limit at x=0

Q: The graph of a function f (x) is shown at right. If g(x) = v5 + 4x , find lim [f(x) + 3 g(x)]. А. 13…

A: Consider the given function: gx=5+4x Consider the given limit expression: limx→1+fx+3gx We can also…

Q: 1. If f(x) = x² + 4x – 5 and g(x) = x – 1, then lim f(x) equals x→1 g(x) с. -1/6 а. -6 b. 6 d. 1/6

A:

Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why. a- Lim 4 c- lim…

A: See the details solution in below

Q: Find the limits. f(x) = x + 4 g(x) = x² %3D (a) lim, f(x) %3D (b) lim g(x) * X--4 %3D (c) lim…

A: Given,            fx=x+4 , gx=x2

Q: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

A:

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: lim (In 2x + 5) + 4 X→ー1

A: Solution:limx→-1ln2x+5+4=ln2-1+5+4

Q: Suppose that f(x) = 1 if x 0. Does lim,→0 f(x) exist? (Draw a picture.) O No, because the limits…

A: Given, limx→0-=1limx→0+=2 Hence, limx→0fx does not exist  since both the limits are not the same.…

Q: 1. Complete the table of values to determine the limits of the function. f(x) = = -1-0.5 -0.1 -0.01…

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

Q: From the graph: (x) is discontinuous at x= 3 because of (a) Lim f(x) = f(3) (b) Lim f(x) doesn't…

A: According to graph at x = 3

Q: -2-1 1 2 3 4 5 -2+

A: We have to find the limit limx→4fx

Q: V+4 -2 Use a table of values to estimate the value of the limit of lim f(x) S(x) 2.

A: Evaluate the limit function

Q: lim -2)2 x-2 x2-4 3.)

A:

Q: 1 1 Find the limit lim *+5 8 x→3 x-3

A:

Q: If lim as t approaches 4 of the function ((g(x)-6)/(t-1))=1. Find lim t approaches 4 of g(t).

A: The given function is ((g(x) - 6) / (t - 1))  As limit t approaches to 4 the value of the function…

Q: Find the limit algebraically. f(-9 + h) – f(-9) lim h-0 where f(x) = – 7x² + 8x – 6 h

A: Given: limh→0f(-9+h)-f(-9)h where f(x)=-7x2+8x-6

Q: Calculate the limit algebraically. x² – 12x +35 lim x2 - 5x →5 O -0.4 O-2 -2.4 O 10

A:

Q: Use numerical or graphical evidence to determine the left and right hand limits of the function. |4…

A:

Q: It was determined that the lim f(x) = 0 and f(2) = 0. Can it be concluded, definitively, that f'(2)…

A:

Q: Find the limit of f(x)

A: Given information

Q: 1. Evaluate lim (2x-5) given its graph below. X-2 b. -1 c. 2 d. 1 а. О 2. Given the graph of f(x)…

A:

Q: 22 - 3x + 2 1 3. Find lim as g3 - 2x2 (a) a→0+ (b) T 2+ (c) 2 (d) 2 (e) What if anything can be said…

A:

Q: The value of the constant k such that x2-kx+7 lim exits is x-1 x+1 -7 7 -8 8 -6

A:

Q: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

Q: Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) X→-1

A: A limit tells us the value that a function approaches as that function's inputs get closer and…