7. Let a be a nonzero real number. Evaluate lim o f (x) and lim,→ f(x), where -00 f (x) = a.x° – 3x* + 6x³ – 7x² + 10. State a result that guarantees the existence of a real root of the polynomial f(x) given the limits above. What would go wrong in this argument if we replace f(x) with a polynomial of an even degree?

Q: Evaluate lim h→0 1 2 3(x+h) ² h 1 3x²

A:

Q: 2. Find lim (√x + 2 = √2).

A:

Q: find lim (2 x3 - 3 x + 5) X --> -1 O 6 O none of these answers O 4

A:

Q: 4) Calculate lim (√t-3, V-2, tan t-4 t-4 (-)). HINT: On the second component, you can factor t - 4…

A: To find:-

Q: 2.x2 + x – 2 7. Compute lim Justify your answer A number is not 7x2 – 3x +1 enough.

A: The objective  is computing the above limit.

Q: What is the inverse of the function y = 9x2 + 12x +4? What domain restrictions are necessary?…

A: Given y = 9x2+12x+4let inverse of y = f-1(x)

Q: x2 + 2x – 1 1 True or False: lim x – 9 4 O True False

A:

Q: a) Evaluate V9x(x² – 3x +2) lim (3х — 3)

A: To find the limit:

Q: a.Show that 30x^3-20x^2-10 is O(x^3). b. Explain what it means for a function to be Ω(1) and give…

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

Q: Evaluate lim h→0 1 2 5 (x+h) ² 2h 1 5x²

A:

Q: Evaluate  lim

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Q: As x→ 2+, x? and x2 · 4 → x2 So the lim x → 2+ 4 Therefore, the line x = is a vertical asymptote.

A: Solve the following

Q: 6. The radical function fx) = √√x is graphed below, along with a few key points. Sketch the…

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.