4) Let lim f(x) = 7, and lim g(x) = 6. Find lim 37) g(x)

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: 4) evaluate lim x-->2 (2x2 - x - 6) / (x2 - x - 2)

A: Explanation of the solution is given below...

Q: 3. If lim f(x) = 5 and lim f(x) = 5, what can you say about x1 X1+ lim f(x)? What can you say about…

A: Definition used -       Limit of a function -       The limit of a function at point x=a…

Q: 7ーズ 1. Find lim using a. Table of values f(x) b. Limit rules

A:

Q: 2. Construct a table of values to investigate 1 if x -1

A:

Q: 4-If. 2-x < flx) < 2Cos(x) for all x then find: lim f(x)

A:

Q: Find the value of -1 tan (5x) lim- X

A:

Q: 2. Evaluate the limit: TC 1000 lim x-7- (x-7)2 lim x→8+ (8 - x)3

A: the given limit is: limx→7-πx-72-limx→8+10008-x3 we have to evaluate the given limit.

Q: Compute:

A: Given: limx→6 f(x)=4

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

A:

Q: Suppose that lim f(x) = 3 and lim g(x) = 5. Then lim g(x). %3D %3D X2 X2

A: Given: limx→2fx=3 and limx→2gx=5. To find: limx→2fxgx2+2fxgx Solution: Product rule of limit states…

Q: Prove that limxc f(x) = Lis equivalent to limxc [ f(x) − L] = 0.

A:

Q: Prove using formal definition. (a) lim x→0+ 1/x = ∞.

A: Draw the graph of the function .

Q: Find the lim x-->0 (x2-x)/(x2+x)

A: We have to find the limit                                      limx→0x2-xx2+x

Q: Evaluate the limit. 1-x² lim *+1 sin(27x) a) lim b) x+2x² C) lim - - 2x *→(π/2)- (2-) tan r Show all…

A:

Q: 3. Use the precise definition of a limit to prove lim(9 – x) = 5

A:

Q: Prove, using the formal definition, that limx→−1 3/(x+1)^2 = +∞

A: We will prove the problem, using the formal definition.

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. - (a) lim sin (2x 6)…

A: solution is given below

Q: Find the limit. lim (2 – x)7 tan(=) x→1

A: It is asked to evaluate the given limit. For solving the problem we need to know some basic…

Q: Prove, using the formal definition, that limx→ 8 [(x)^1/3 = 2.]

A: The definition of limit is  limn→∞an=l foe each ε&gt;0, there is a positive integer N such that…

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: Once you know lim x--&gt;a+ f(x)  and lim x--&gt;a-  ƒ(x) at an interior point of the domain of ƒ,…

A: If we know the right and left-hand limit of a point then we know the limit at that point.

Q: Determine the infinite limit. X 1 lim x4+ X - 4 -CO

A: We will plug x=4^+ in the expression first. We got 0 in denominator. So lets check by plugging…

Q: What is lim x-->2 f(x)

A: Here we will see the graph and answer as per that....

Q: How do you solve question 11 and 12?

A: (11)Given:

Q: 1. Evaluate the limit: 5 - x lim x→5+ (x – 5)2

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

Q: 4. Using the precise definition of a limit, prove lim (2x +8) = 38. x-15

A:

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. (a) lim sin (2x6) sin(4x…

A: Explanation of the answer is as follows

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: Evaluate lim-[(sinx-x)/x³] by u

A:

Q: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

A:

Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

A:

Q: Suppose that ƒ is an odd function of x. Does knowing that lim x--&gt;0+ ƒ(x) = 3 tell you anything…

A:

Q: If f and g are two functions such that lim f(x) as x --> a = + infinity and lim g(x) as x --> a = +…

A: Given: f &amp; g are two functions such that, To check if this statement is True or False

Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: find the limit of lim x->3 sin(x-3)/x^2-x-6

A: To find limx→3sinx-3x2-x-6

Q: 4-If. 2-x s flx) < 2Cos(x) for all x then find: lim (x)

A: Given: 2-x≤f(x)≤2 cos(x)

Q: How do you solve question 5 and 6?

A:

Q: Evaluate lim (e* – 2.x) x→0-

A: To evaluate: limx→0-(e3x-2x)3x

Q: 3- If lim f(x) = 3.5 and lim,2+ f(x) = 6.5 , the function has a double sided x-2- limit or one sided…

A:

Q: lim x in (It -)

A:

Q: 3. Show algebraically that lim x* – 2 – x = 0

A:

Q: 9. Find the indicated limit. lim (6x - 21)³ x-4 = Show any work necessary

A: Solution: As per given data   lim( x tens to 4){ (6x - 21)³} As per simple rule of limit go ahead…

Q: Use basic techniques to find the limits. 8. lim(-7) X-3 9. lim (x³ + 2x) X→-1 10. lim cos x

A:

Q: Find the limits limx→0+x tan (π/2 - x)

A: Given that, f(x)=x tan (π/2 - x) We have to find, limx→0+xtanπ2-x

Q: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

A:

Q: 5. Find the limit of lim x* +0-x

A: Topic = Limits

Q: Use e-5 definition and prove that lim (2 5r) -6

A: Here we use basic definition of epsilon and delta .

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.