Bihar Board Class 12 (Commerce) Continuity and Differentiability — practice questions
87 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Bihar Board Class 12 (Commerce) Continuity and Differentiability in the app →The derivative of $ in(3x)$ is:A function whose graph can be drawn without lifting the pen is:If f is not continuous at c, then c is called a point of:If a function is differentiable at a point, it is also:The rule for differentiating a composite function is the:f(x) = x squared at x = 0 is:Functions written with y not isolated are called:Continuity of f at c requires the limit at c to equal:Theorem 1 concerns two functions that are both:Theorem 2 deals with which kind of function?Theorem 3 says differentiability at a point implies:Does continuity at a point guarantee differentiability?The chain rule can be extended to composites of:An alternative to repeated product rule for many factors is:For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:The function f(x) = |x| at x = 0 is continuous but not:To differentiate an implicit relation you use the:A function that fails the limit test at a point is:Composites of continuous functions, by Theorem 2, are:A function f is continuous at x = c when f(c) equals which quantity?Every differentiable function is necessarily which of the following?Differentiate sin(x^2) with respect to x.The natural log's derivative is which function?For x in (-1, 1), the derivative of sin^-1 x equals which expression?The derivative of sin^-1 x exists only for x in which set?If t = u(x) and f = v o u, the chain rule gives df/dx as what?Find d/dx of (2x + 1)^3.Find the slope function of y = (2x + 1)^100.At which real numbers is every polynomial function continuous?A rational function p(x)/q(x) is continuous at every x where what holds?The greatest integer function [x] is discontinuous at which points?The function f(x) = |x| is continuous everywhere but at x = 0 it is not what?For f(x) = |x|, what are the left and right derivatives at 0 respectively?In the parametric form x = f(t), y = g(t), what is t called?Given x = a sin t and y = a cos t, find dy/dx.Given x = a t^2 and y = 2a t, dy/dx is which?Parametrically x = t^2, y = t^3 (t nonzero); find dy/dx.If y = a^x with a > 0, find y'.By logarithmic differentiation, d/dx of x^x (x > 0) equals what?For y = x^(sin x) with x > 0, which expression gives dy/dx?At x = 1, the derivative of y = x^x has which value?For x^3 + y^3 = a^3, what is dy/dx?From 2x + 3y = sin x, obtain dy/dx.Find y' where x^2 + xy + y^2 = 100.For x^2 + y^2 = 25, find dy/dx at the point (3, 4).If sin^2 x + cos^2 y = 1, what is dy/dx?Which symbol denotes the second order derivative of y in x?Evaluate the second derivative of x^3 at x = 2.Find y'' for y = sin 2x.Evaluate y'' for y = log x.For y = A sin x + B cos x, which expression equals zero?For y = 3e^(2x) + 2e^(3x), which relation is satisfied?For y = sin^-1 x with first and second derivatives y1 and y2, which holds?Find d(sin x)/d(e^x).Compute d/dx of e^(-x).Find the rate of change of sin(log x) as x varies.If y = e^(cos x), find y'.If y = cos^-1(e^x), what is y'?Is the equation x = e^(log x) true for every real x?For f(x) = (1 + x)(1 + x^2)(1 + x^4)(1 + x^8), what is f'(1)?A real function is called continuous when it is continuous where?For f to be continuous on [a, b], what must hold at the endpoint a?If f and g are continuous at c, which combinations are continuous at c?When is f/g continuous at c, given f and g continuous there?If g is continuous at c and f is continuous at g(c), what follows for f o g?Why is sin(x^2) continuous at every real number?tan x is continuous on its domain. Which point is outside that domain?Where is the sine function continuous?Find k making the map kx^2 (x <= 2), 3 (x > 2) continuous at 2.A map uses kx + 1 up to 5 and 3x - 5 after; continuity at 5 forces k = ?What f(3) closes the gap in (x^2 - 9)/(x - 3) at x = 3?What f(0) fills the gap in sin(5x)/x at the origin?f(x) = 2x + 3 for x <= 2 and 4x - 1 for x > 2: what holds at x = 2?f(x) = x^2 + 1 for x < 1 and 3x - 1 for x >= 1: at x = 1, f is what?A map is x^2 up to 1 and 2x - 1 beyond; how does it behave at 1?For f(x) = x|x|, what is the derivative f'(0)?Is f(x) = |x - 2| differentiable at x = 2?A continuous f on [0, 1] has f(0) = -2 and f(1) = 3. Which theorem gives a zero?A continuous function on a closed interval [a, b] always attains what?The Dirichlet function, the indicator of the rationals, is continuous at how many points?The derivative of f at c is defined as which limit?A function is Lipschitz continuous if there is a constant K such that what?Continuity at c needs which three quantities to be equal?Find the third derivative of x^4.Find y' when y = log(1 + x^2).Evaluate d/dx of the function e^(x^2).Give the slope function of log(sin x).