CBSE Class 11 (Commerce) Limits and Derivatives — practice questions
86 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 11 (Commerce) Limits and Derivatives in the app →The derivative of $ in x$ is:The famous standard limit lim_{x→0} (sin x)/x (with x in radians) equals:The expression 0/0 is called:Using the QUOTIENT rule, d/dx [f(x)/g(x)] equals:Using the CHAIN rule, d/dx [sin(3x)] equals:The derivative of the natural logarithm function, d/dx [ln(x)] equals:A function f is continuous at x = a if and only if:The function f(x) = |x| at x = 0 is:The TANGENT line to y = x² at the point (2, 4) has equation:Limits and derivatives form the introduction to:Approaching a point from either side gives limits numbering:The value expected from points to the right of a is the:The value expected from points to the left of a is the:If the two one sided limits coincide, that common value is the:If the two one sided limits differ, the limit at that point:To find a limit at 5, one looks at values of x that are:A limit describes the behaviour of a function:The derivative of a function at a point is defined using a:The definition of derivative applies to a function that is:Defining the derivative directly from the limit is called the:The derivative exists at a point only if the limit:The derivative at a point gives the slope of the:Velocity at a single instant of time is called:Instantaneous velocity is found by taking a limit of the:For the function x plus 10, the limit at 5 works out to:Points such as 4.9, 4.95 and 4.99 lie to the left of:A limit is concerned with the value a function is:Derivatives are defined at a point lying in the function's:The two one sided limits of a function are compared to test:Reading the derivative as a rate of change describes how fast a value:The first principle finds a derivative without using any:A stone falls so that its distance is s = 4.9t^2 metres. What is its exact speed at t = 2 s?A body falls with s = 4.9t^2 metres. Find its average velocity over the first 2 seconds.For s = 4.9t^2 metres, what is the average velocity between t = 1 s and t = 2 s?Geometrically, the instantaneous velocity from a distance-time curve equals what?Velocity is the rate of change of which quantity?Calculus mainly studies which of the following?As x gets closer and closer to 0, which value do the numbers x^2 approach?Which limit does g(x) = |x| (x not 0) approach as x tends to 0?The right hand limit of f at a is decided by x values that are what?Take f(x) = 1 when x <= 0 and f(x) = 2 when x > 0. Which value does f approach from the right of 0?When does the limit of f(x) as x tends to a exist?Two functions approach 3 and 4 at a point a. Which value does their product approach there?Given limits 7 for f and 2 for g at a, what limit does the difference f minus g have?Near a point, one function approaches 10 and another approaches 4. Their ratio approaches what?A function is f(x) = x + 10. Which value does f approach as x draws near 1?Which value does the polynomial x^2 + 3x - 1 settle toward when x approaches 2?The rational expression (x + 1)/(x + 4) is evaluated for x creeping toward 2. What value is approached?For p(x)/q(x) with q(a) = 0 but p(a) not 0, what happens to the limit at a?What value does (x^2 - 9)/(x - 3) approach when x closes in on 3?If x = a makes both top and bottom zero, what should be tried first?For any positive integer n, what is the limit of (x^n - a^n)/(x - a) as x tends to a?By the standard result for (x^n - a^n)/(x - a), what does (x^3 - 8)/(x - 2) approach at x = 2?A ratio (x^15 - 1)/(x - 1) is studied near x = 1. What value does it tend to?If f(x) <= g(x) near a and both limits exist, which relation holds?If f(x) <= g(x) <= h(x) and f and h both tend to 5 at a, what does g tend to?For x measured in radians, what value does sin x divided by x approach near 0?Which value does (1 - cos x)/x approach near x = 0?Which identity is used to find the limit of (1 - cos x)/x at 0?Near x = 0, which constant does the ratio sin 3x over x approach?Which value is approached by tan x divided by x when x is nearly zero?When x is nearly zero, the ratio of sin 5x to sin 3x approaches which value?Which expression defines the derivative f'(a) at a point a?Using the definition, find the derivative of f(x) = 3x at x = 2.Find f'(-1) for f(x) = 2x^2 + 3x - 5.What is the derivative of a constant function at any point?The derivative of f at a point P gives which geometric quantity?As Q approaches P along a curve, the chord PQ tends to which line?Finding a derivative using the limit of the difference quotient is called what?Which notation can stand for the derivative of y = f(x) with respect to x?What is the derivative of f(x) = x^2 from first principles?The derivative of f(x) = a, a fixed real number, is what?Which statement is the sum rule for derivatives?The Leibnitz rule for the derivative of a product (uv)' is which expression?Which formula gives the derivative of the quotient u/v?What is the derivative of x^n for a positive integer n?Differentiate x^100 with respect to x.Does the rule d(x^n)/dx = n x^(n-1) hold for negative or fractional n?Differentiate 6x^100 - x^55 + x.Find the derivative of (x + 1)/x for x not equal to 0.Which function results when sin x is differentiated?Differentiating tan x yields which expression?Evaluate f'(10) when f(x) = x^2 - 2.What is the slope of the tangent to y = x^2 at the point where x = 3?Differentiate x^2 sin x using the product rule.Find the derivative of 7x^3 with respect to x.