Explore L'Hospital's Rule in calculus through a comprehensive video tutorial. Dive into various limit problems, including trigonometric, exponential, and logarithmic functions. Learn to apply L'Hospital's Rule to solve complex limits as variables approach zero, infinity, or other values. Practice with examples from James Stewart's Single Variable Calculus textbook, covering topics such as limits of quotients, products, and compositions of functions. Gain insights into special cases and potential pitfalls when using L'Hospital's Rule. Enhance your problem-solving skills with a wide range of exercises, from basic applications to more challenging scenarios involving multiple applications of the rule.
Overview
Syllabus
Q109, limit of cos(x)/(1-sin(x)).
Q110, limit of (e^(2t)-1)/sin(t) as t goes to 0.
limit of ln(x)/sqrt(x) as x goes to infinity, L'Hospital's Rule.
limit of (8^t - 5^t)/t as t goes to 0, L'Hospital's Rule.
limit of (e^x-1-x)/x^2 as x goes to 0, L'Hospital's Rule.
Q118, limit of (ln(x))^2/x as x goes to infinity, L'Hospital's Rule.
limit of x^3*e^(-x^2) as x goes to infinity, L'Hospital's Rule.
limit of x*tan(1/x) as x goes to infinity, L'Hospital's Rule.
Q114, Limit of x/(x-1)-1/ln(x) as x goes to 1, L'Hospital's Rule.
Limit of 1/x-1/(e^x-1) as x goes to 0+.
Q111, Limit of ln(x^7-1)-ln(x^5-1) as x goes to 1+.
Limit of (1-2x)^(1/x) as x goes to 0, L'Hospital's Rule.
Limit of (1+sin(4x))^(cot(x)) as x goes to 0+, L'Hospital's Rule.
Q122, Limit of ln(x)/x^p as x goes to infinity, L'Hospital's Rule,.
Q120, Be Careful with L'Hospital's Rule.
Q117, 0^inf vs inf^0.
Q116, Limit of x^(1/(1-x) as x goes to 1+, L'Hospital's Rule.
limit ln(x^8-1)/ln(x^2-1) as x goes to infinity, L'Hospital's Rule.
limit (tan(x)-x)/x^3 as x goes to 0, L'Hospital's Rule.
limit ln(x^8-1)-ln(x^2-1) as x goes to 1+, L'Hospital's Rule.
limit of ln(x)/x as x goes to 0+, do we need L'Hospital's Rule?.
Q119, limit of e^x*sin(1/x) as x goes to infinity.
Limit of ln(x^7-1)/ln(x^5-1) as x goes to 1+.
L'hospital Rule: limit of x^p*ln(x).
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