Question 1 (a) Limits of functions are evaluated using many different techniques, such as recognizing a pattern, simple substitution or using algebraic 1 simplification. Evaluate lim *+2 2. X2 x-2

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

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

Q: Suppose that ƒ is an even function of x. Does knowing that lim x-->2- ƒ(x) = 7 tell you anything…

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Q: Sketch the graphs of functions that have the given limits and values. lim f(x)= infinity x-->2-, lim…

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Q: Create a table of value (use 8 values- 4 on the left and 4 on the right) and a calculator to the…

A: topic- limits

Q: EXAMPLE 9 Using Substitution Find lim sin (1/x).

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Q: 1 Find lim - and lim 1 x→-0 x

A: This question is taken from the limit in which we have to find the limit of the given question. We…

Q: Evaluate lim x->-1 if f(x) {  1/x if x < -1                          { x2 - 2 if x ≥ -1

A: To evaluate: The limit limx→-1fx. Given: The function is fx=1x,        If x&lt;-1x2-2    If x≥-1.…

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?

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Q: Let ƒ(x) = (x2 - 1)/(| x| - 1). a. Make tables of the values of ƒ at values of x that approach c =…

A: a) When x is near -1 then x is negative.  For negative x, we have |x|=-x Using this we simplify the…

Q: Which will best solve lim *-6x+9, х-3 x-3 O Derivatives O Limits of a function O Indeterminate forms…

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Q: Create a table of values for the function and use the result to estimate the limit. Use a graphing…

A: Create a table of values for the function as follows: x x4-1x6-1 0.98 0.994-10.996-1=0.67334…

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

A: WE HAVE TO FIND THE VALUE OF THE GIVEN LIMIT    THE GIVEN EXPRESSION IS limx→∞2+x2-x

Q: Sketch the graph of any function that satisfies the given conditions. x-intercept at -1 and…

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Q: What are limx→+-∞ k (k a constant) and limx→+-∞ (1/x)? How doyou extend these results to other…

A: limx→af(x)=L means f(x) becomes arbitrarily close to L as long as x is sufficiently close to a.  We…

Q: Numerically estimate accurate to 2 decimal places of lim x -> 0 ((2^x -1)/(x))

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Q: Find the limit. Use a graphing utility to verify your result.

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Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

Q: 10* – 5* – 2* +1 (b). Evaluate lim- VI+x-V1-x (i).Evaluate lim- sin-!

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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: lim x approaches 1  .... [(x^-1) - 1]/(x -1)

A: Consider a limit limx→afxgx. The conventional evaluation of the limit sometimes lead to…

Q: Find the limit when x-> 0 lim(√x+11-√11)/x

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Q: x³-8 4 x+2 x 16 2. lim

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Q: Show that

A: Here we have to show that;  limx→-∞1x

Q: 23. lim -3 X-3 -/3

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Q: 7x - 49 -if it exists. If the limit does not exist explain why. Justify each step by Find lim -7 x-…

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Q: lim (In x)

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

Q: How do you solve question 11 and 12?

A: (11)Given:

Q: Find the limit of each function lim   8x^2 / cos x - 1 x - > 0

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Q: lim F(x),

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Q: sinx Example 11: lim nx X X-

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Q: tan(x) 5. Compute the limit for lim x-0 sin(x) , and show by hand how MAPLE obtain the results.

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Q: By squeeze theorem, how to evaluate lim x->0 x^2 sin (6pi/ cube root x)

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Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim 20…

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Q: 6. Without graphing the function on your calculator, find the limit. Use L'Hopital's Rule where…

A: Solution of the problem as follows

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

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Q: Suppose that ƒ is an even function of x. Does knowing that limx →2- ƒ(x) = 7 tell you anything about…

A: Even functions are symmetric about the y-axis for example: if we know f(1.99) then f(-1.99)=f(1.99)…

Q: Find the limit.  lim x--> infinity  ln (3x2-1/x2+1)

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Q: ure E-S theorem to prove the following lim (9x+5) = - 32. x→3

A: Here we will evaluate the required value.

Q: lim x in (It -)

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Q: 1) If lim f(x) = , what asymptotic behavior will be illustrated in the graph of f (x)?

A: 1) If limx→6-fx=∞, then the value of the function fx tends to infinity as x→6 from the left hand…

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Q: EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

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Q: Find the limit.

A: Given,

Q: 1 Evaluate lim (csc x)*-

A: We have to solve

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A: We have to evaluate the limit limx→1x4-1x6-1 using a table of values for the function. Making a…

Q: Find the limit. Use a graphing utility to verify your result.

A: