AP EAPCET (Engineering) Limits — practice questions
75 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Limits in the app →What number does (x^2 - 4)/(x - 2) approach as x nears 2?For x in radians, the ratio sin x / x settles at which value as x shrinks to 0?Find the limiting value of tan x divided by x when radian x goes to zero.As x tends to 0, the ratio sin(5x) over x approachesCompute the limit at 0 of the quotient sin 3x divided by sin 5x.The standard limit of (e^x - 1)/x as x tends to 0 equalsNatural log of (1 + x), divided by x, tends to what as x goes to 0?The limit of (1 + x) raised to 1/x as x tends to 0 is the numberWhat does (1 + 1/x) to the power x approach as x grows without bound?If f(x) = x + 3, f(x) gets nearer to which value as x gets nearer to 3?Let g(x) = (x cubed - 1) over (x - 1). What value does g approach near x = 1?The expression (x^3 - 8)/(x - 2) has what limiting value as x approaches 2?Near x = 0, the value of (1 - cos x) divided by x squared settles atAs x tends to zero, (1 - cos x) divided by x (first power) tends toWhen x becomes enormous, 1/x moves towardFor huge x, the fraction (3x + 2) over (x - 1) is close to which number?Determine the end behaviour of (2x^2 + 1)/(x^2 + 5) as x goes to infinity.Rationalise to find the limit of (root x - 2)/(x - 4) as x nears 4.Multiplying by a conjugate, the ratio (root(1+x) - 1)/x tends to what at 0?At x near zero, the quotient (e^(3x) - 1)/x approachesThe ratio (2^x - 1)/x converges, as x goes to 0, toThe ratio tan(2x) over x has what limit at x = 0?Close to zero, sin(2x) divided by 3x approachesWhat value does cos x take in the limit as x tends to pi?A function equals 3x + 1 below x = 1 and 7x^2 - 3 at or above 1. Its limit at 1 isFor the greatest integer function [x], the left-hand limit at x = 3 isConsider f(x) = |x|/x near the origin. What is true of its limit at 0?The absolute value |x| has what limit as x tends to zero?Suppose f tends to 2 and g tends to 5 as x tends to a. Then f + g tends toWith f tending to 2 and g tending to 5 at a, the product f times g tends toAfter cancelling x, the quotient (x^2 + 3x)/x tends to what at x = 0?Find the number that (root(x + 9) - 3)/x approaches when x is close to 0.After factorising, (x^2 - 1)/(x^2 + 3x - 4) tends to what as x goes to 1?The fraction (x^2 + x - 2)/(x + 2) heads to what number as x nears -2?Squares differ: (x^2 - 9)/(x - 3) has which limiting value at x = 3?Let h(x) = (x^2 - 25)/(x - 5). What does h(x) approach as x tends to 5?Evaluate (e^x - e^(-x))/x in the limit where x goes to zero.A ratio of cubics, (5x^3 - 2)/(2x^3 + 7), tends to what as x goes to infinity?For very large x, (4x^2 + x)/(x^3 + 1) is closest toSquaring the ratio sin x / x, the limit of sin^2 x / x^2 at 0 isRewrite tan x - sin x as tan x (1 - cos x). Then (tan x - sin x)/x^3 tends toUsing a double-angle identity, (1 - cos 2x)/x^2 has what limit at zero?The quotient (1 - cos 4x)/x^2 approaches which value as x shrinks to 0?A difference of sines, (sin 4x - sin 2x)/x, tends to what at x = 0?As x tends to 0, (1 + 3x) raised to the power 1/x approachesFor x growing without bound, (1 + 2/x)^x approachesSplit (3^x - 2^x)/x into two standard parts. Its limit at x = 0 isUsing the power-difference rule, (x^5 - 32)/(x - 2) tends to what at x = 2?If x is in degrees instead of radians, sin x / x tends to what as x goes to 0?In the epsilon-delta definition, closeness of x to a is written asA limit at infinity needs a number M such that |f(x) - l| < epsilon for allAn infinity over infinity form at infinity is handled by dividing byFactorise top and bottom of (x^2 + x - 6)/(x^2 - 4). Its limit at x = 2 isWhy does a limit at x = a ignore the value of f at a itself?A function with no abrupt jumps in its value is calledWhich function is continuous at every real number?A rational function is discontinuous only where itsf(x) = 1/(x - 4) is discontinuous at x equal toThe height of a growing flower over time is a good example of aMoney in a bank account over time is discontinuous because itf is continuous at x = c exactly when the limit as x tends to c equalsIf f(x) = (x^2 - 9)/(x - 3) for x not 3 and f(3) = k is continuous, k isThe sinc function sin(x)/x is made continuous at 0 by defining its value there asThe Heaviside step function has what kind of discontinuity at 0?The intermediate value theorem needs f to be continuous on aA child grows from 1 m to 1.5 m in four years. By the IVT, height 1.25 mThe IVT guarantees that x^3 - x - 1 = 0 has a root in the intervalA function is right-continuous at c if no jump occurs when x approaches c from theEvery differentiable function at a point is alsof(x) = |x| is continuous at 0 but at 0 it isf(x) = x sin(1/x) for x not 0 is made continuous at 0 by setting f(0) toIf f(x) = 2x + 1 for x < 1 and f(x) = ax + 2 for x at least 1 is continuous, a equalsBy the squeeze theorem, the limit of x^2 cos(1/x) as x tends to 0 isWhich definition was introduced to formalise continuity?A continuous function on a closed interval [a, b] attains a maximum by the