Suppose that f(r) and g(r) are polynomials in x and that lim, . fx)/g(x)) = 2. Can you conclude anything about lim, „-- --~ (f(x)/g(x))? Give reasons for your answer.

Q: 1. Let f(x)= x²+x-6 |x2| 7 x b 2 x + a 3 2 if x 2

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Q: If f' (r) exists, then lim, r f(x) = f(r)

A: given, f'(r) exists  then we tell about limx→rf(x)=f(r) is true or not

Q: b. Find lim (xv (xVx²+1-x²)

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Q: Viewed as a function f: R → R, a polynomial of odd degree is always surjective. True False

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Q: If is a polynomial, show that  lim x->ap(x)= p(a).

A: Let us consider the nth degree polynomial  px=anxn+an-1xn-1+-----+a1x+a0where a0, a1, ......, an∈R…

Q: Viewed as a function f: R → R, a polynomial of even degree is never injective. True False

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Q: Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove…

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Q: Let p (x) be a polynomial. Then limn->o∞ p(n) O Cannot be determined

A: Topic:- calculus

Q: 1. Describe how to find the limit of a polynomial function p(x) as x approaches c.

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Q: Apply Corollary 2 to the Intermediate Value Theorem. f is a polynomial and continuous everywhere.…

A: Given that, f(-3) = 170 > 0 f(-2) = -25 < 0 f(-1) = 2 > 0 f(0) = -1 < 0 f(l) = 2 > 0…

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Show that f (a) = is Libschitz function on r+ 2

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Q: Find lim (V + 1 - Vĩ).

A: To find the limit

Q: Let a be a real number. Then [lim, a f(x)] [lim, »a 9(x)] = lim, a [f(x)g(x)]. x→a

A: Given,          Let α be a real number . Then limx→αfx limx→αgx=limx→αfxgx.

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.