L’ Hospital’s Rule:
The limit (x→a) {f(x) / g(x)} is in general equal to the limit of the numerator divided by the denominator.
But when limit (x→a) f(x) or limit (x→a) g(x) are both zero or ∞, the quotient takes the form (0/0) or (∞/∞) which is meaningless.
This limit can be evaluated by L’ Hospital’s Rule.
If f(x) and g(x) are two fractions of x such that
(i) limit(x→a)f(x)=limit(x→a) g(x) = 0 (or ∞)
(ii) both are continuous at x = a
(iii)both are differentiable at x =a
(iv) both f ‘(x) and g ‘(x) are continuous at x = a, then
limit (x→a) {f(x) / g(x)} = limit (x→a){f ‘(x)/ g ‘(x)}
provided g ‘(x) ≠ 0
Click here to open MCQs of L’ Hospital’s Rule in Google Form
Solutions of MCQs of L’ Hospital’s Rule are given below. I suggest you give the test first in Google Form and then go through the solution. That way you will understand better what you have done wrong.
Solutions of MCQs of L’ Hospital’s Rule
L Hospitals Theorem 1Solutions to questions 4 and 5 are given below.
L Hospitals Theorem 4Solutions to questions 6, 7, 8 are given below.
L Hospitals Theorem 6Solutions to questions 9, 10, 11 and 12 are given below
L Hospitals Theorem 9Solutions to questions 13, 14 and 15 are given below.
L Hospitals Theorem 10 Formula Mathematics
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