Suppose that ƒ is an even function of x. Does knowing that limx →2- ƒ(x) = 7 tell you anything about either limx → -2- ƒ(x) or limx → -2+ ƒ(x)? Give reasons for your answer.

Q: is it true that ∇f(limx)=lim∇f(x) and further that ∇2f(limx)=lim∇2f(x)?

A: We know,  ∇f(xi)=f(xi)-f(xi-h), h=xi-x0i,i=0,1,2...And…

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

A:

Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: Suppose that ƒ is an odd function of x. Does knowing thatlimxS0+ ƒ(x) = 3 tell you anything about…

A: A function f said to be an odd function if it follows the property f-x=-fx. Since given function f…

Q: Show by means of an example that limx->a [f(x) + g(x) ]may exist even though neither  limx->a…

A:

Q: Compute:

A: Given: limx→6 f(x)=4

Q: What is lim f(x)? X-1

A: Given graph: To Find: limx→1f(x)

Q: If lim as f(x)-4/x-3=2 as x approaches 5, find lim f(x) as x approaches 5.

A: We have

Q: Let ƒ(x) = (x^2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01,…

A: Consider the given function:

Q: What is lim ? X-0+ x

A:

Q: Find Limit Using Squeeze Theorem: 2. If 2x – 2s f(x)<x² – 4x + 3 for x 2 0, find lim f(x).

A:

Q: Suppose neither limx→0 f(x) nor limx→0 g(x) exists. Show that limx→0 [f(x)g(x)] may exist.

A:

Q: If ƒ(1) = 5, must limxS1 ƒ(x) exist? If it does, then must limxS1 ƒ(x) = 5? Can we conclude anything…

A: A function f(x) is said to be continuous at a point x = a, in its domain if the following three…

Q: Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c =…

A: Given: Fx=x2+3x+22-x To determine: We have to estimate limx→-2Fx by making a table of values of F at…

Q: Suppose that ƒ is an odd function of x. Does knowing that limx →0+ ƒ(x) = 3 tell you anything about…

A: Given that f(x) is an odd function.  So, f(-x)= -f(x) Given that lim x →0+ ƒ(x) = 3

Q: Find a number b such that lim- .2. x²-4 =2 x-b x-x -2

A:

Q: Let ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01,…

A: Simplify f(x) first for x not equal to -3 x y -3.1 -6.1 -3.01 -6.01 -3.001 -6.001…

Q: Suppose that ƒ(x) and g(x) are polynomials in x and that lim

A: We have given fx and gx are polynomials in x and limx→∞fxgx=2.

Q: Find the value of * lim - 1 - 1 1 +x

A: Let us take f(x)=x11+x-1. Then we have to find limx→0f(x).

Q: Sketch the graph of the function and use it to determine the values of a for which limx--a f (x)…

A: We will find out the required values.

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: Sketch the graph of a function f (x) that satisfies the following conditions: limx -→ -o f (x) = o ;…

A: Follow the steps to sketch the graph.

Q: Let ƒ(x) = (x2 - 9)/(x + 3). Make a table of the values of ƒ at the points x = -3.1,-3.01, -3.001,…

A: Given, fx=x2-9x+3   x=-3.1 x=-3.01 x=-3.001 x=-3.0001 x=-3.00001 fx=x2-9x+3 -6.1 -6.01 -6.001…

Q: Give examples of functions f(x) and g(x) with limx→∞ f(x) = ∞ and limx→∞ g(x) = 0

A: We want to find two functions f(x) and g(x).

Q: 4. If lim f(x) = -2, lim f(x) = 3, and f(0) = -2, what can X0+ X0- you say about lim f(x)?

A: Given, limx→0+f(x)=-2limx→0-f(x)=3f(0)=-2     Find limx→0f(x)

Q: Given f(x) = 3/(4-x)3 , evaluate limx=4+ f(x)

A:

Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

A:

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find lim x→ -2 (-4p(x) +…

A: Given limx→-2p(x)=-4 , limx→-2r(x)=0 and limx→-2s(x)=-3We need to find:limx→-2-4p(x)+5r(x)s(x)

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find lim x→ -2 (p(x) +…

A: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find limx→ -2(p(x) + r(x)…

Q: Suppose limx →4 ƒ(x) = 0 and limx →4 g(x) = -3. Find lim x →4 xƒ(x)

A: It is given that limx→4fx=0 and limx→4gx=-3.

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

Q: Given the function f(x) = sqrt(x-2), please evaluate the limit. limx→∞ f(x)

A:

Q: Suppose that a function ƒ(x) is defined for all real values of x except x = c. Can anything be said…

A: Given: The function fx is defined for all real values of x except x=c, To determine: Whether the…

Q: Let f(x)= -2x^2-x, if x1 Find limx-1- f(x).

A:

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Find limx→ -1 ƒ(x) algebraically.

A: Given f(x)=(x2-1)/(|x|-1). We need to find limx→ -1 ƒ(x).

Q: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

A:

Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

A:

Q: Let f(x)= -7x^2-8x, if x<1 4, if x=1. 5x-2, if…

A: Concept: Left hand limit: The value of a function that approaches when a variable gets close to its…

Q: Show by means of an example that limx-&gt;a [f(x) g(x) ]may exist even though neither  limx-&gt;a…

A: Now,         Let,f(x)=5x−x|x|, g(x)=5x+x|x| :

Q: If 3-2x sf(x)s3-x for -1sxs1, find lim f(x). lim f(x) =|

A: Calculate left hand limit and right hand limit than find the limit using sandwich theorem.

Q: Use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.   limx→8f(x)=

A: To use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.

Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

A:

Q: Use the –δ definition to prove that lim x→1 (3x + 5)/2 = 4.

A:

Q: Let flx)= S2x-1 if x>3 what is lim f(x) ? 2x+2ifX<3, what is lim flx)? メ-3 とラメふとす

A: Given: fx=2x-1if x&gt;3x+2if x≤3

Q: Consider the function…

A: The graph of f is as follows:

Q: Sketch the graph of a function f such that: limf(x)=0 X-7

A: We take a function  f(x)= 1/(x-7)

Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

A:

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: Find the limit or show that it does not exist lim 212 + 3t – 5

A:

Q: Give a specific example of f(x) with limx→∞ f(x)=1 and limx→∞ g(x)=∞ such that limx→∞ f(x)^g(x)=0.…

A:

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.