Questions and Answers on Limits in Calculus
A set of questions on the concepts of the limit of a function in calculus are presented along with their answers. These questions have been designed to help you gain deep understanding of the concept of limits which is of major importance in understanding calculus concepts such as the derivative and integrals of a function. These questions also helps you find out concepts that need reviewing.
Question 1:
Question 2:
and then lim [ f(x)  g(x) ] as x > a is always equal to 0. Answer : False. Infinity is not a number and infinity  infinity is not equal to 0. +Infinity is a symbol to represent large but undefined numbers. infinity is small but undefined number.
Question 3:
Question 4:
The degree of the denominator (2) is higher than the degree of the numerator (1) hence the graph of has a horizontal asymptote y = 0 which is the x axis. But the graph of f has an x intercept at x = 2, which means it cuts the x axis which is the horizontal asymptote at x = 2.
Question 5:
and then (A) lim [ f(x) . g(x) ] as x > a is always equal to 0 (B) lim [ f(x) . g(x) ] as x > a is never equal to 0 (C) lim [ f(x) . g(x) ] as x > a may be +infinity or infinity (D) lim [ f(x) . g(x) ] as x > a may be equal to a finite value. Answer : (C) and (D). Try the following functions: f(x) = 1 / x and g(x) = 2x as x approaches 0. f(x) = 1 / x^{ 2} and g(x) = x as x approaches 0.
Question 6:
Question 7:
Question 8:
Question 9:
More references on calculus questions with answers and tutorials and problems .
