Science:Math Exam Resources/Courses/MATH104/December 2012/Question 01 (l)

MATH104 December 2012

  •  Q1 (a)  •  Q1 (b)  •  Q1 (c)  •  Q1 (d)  •  Q1 (e)  •  Q1 (f)  •  Q1 (g)  •  Q1 (h)  •  Q1 (i)  •  Q1 (j)  •  Q1 (k)  •  Q1 (l)  •  Q1 (m)  •  Q1 (n)  •  Q1 (o)  •  Q2 (a)  •  Q2 (b)  •  Q2 (c)  •  Q2 (d)  •  Q2 (e)  •  Q3  •  Q4 (a)  •  Q4 (b)  •  Q4 (c)  •  Q5 (a)  •  Q5 (b)  •  Q6 (a)  •  Q6 (b)  •  Q6 (c)  •  Q6 (d)  •  

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Question 01 (l)
If f'(a) exists, then $\lim _{x\to {}a}f(x)$ (i) equals f(a). (ii) equals f'(a). (iii) must exist, but may not equal f(a) or f'(a). (iv) might not exist. (v) None of the above.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
If a function is differentiable at a point $x=a$, then it is ___________ at the point $x=a$.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. The fact that $f'(a)$ exists is equivalent to saying that the function $f(x)$ is differentiable at $x=a$. Recall that a function must be continuous at a point to be differentiable at that point. For the function to be continuous at a point $x=a$, the condition $\lim _{x\rightarrow a}f(x)=f(a)$ must be satisfied. Therefore, (i) is the answer.

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