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AP DSC School Assistant Math Model Test 3

Section: Subject Specific

Question : 118 of 160

Marks: +1, -0

\rm \lim_{x\rightarrow a}f(x)=L

\rm \lim_{x\rightarrow a}g(x)=M

\rm \lim_{x\rightarrow a}[f(x)+g(x)]

is equal to:

Solution:

Concept:

The sum rule for limits: If the limits of two functions exist separately, then the limit of their sum is equal to the sum of their individual limits.

Explanation:

We are given:

\lim_{x \to a} f(x) = L

and

\lim_{x \to a} g(x) = M

Using the sum property of limits:

\lim_{x \to a} \bigl[ f(x) + g(x) \bigr] = \lim_{x \to a} f(x) + \lim_{x \to a} g(x)

Substituting the given values:

= L + M

Thus, the required limit equals

L + M

Answer:

Option A:

L + M

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