JEE Main Limits and Derivatives — practice questions
48 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Limits and Derivatives in the app →The value of $\displaystyle\lim_{x\to 0}\frac{ in x}{x}$ is:The derivative of $x^n$ with respect to $x$ is:The derivative of a constant function is:The value of $\displaystyle\lim_{x\to 2} x^2$ is:The derivative of $ in x$ with respect to $x$ is:By first principles, the derivative of $f$ at $x$ is $\displaystyle\lim_{h\to 0}$ of:The derivative of $x^3$ with respect to $x$ is:The value of $\displaystyle\lim_{x\to 0}\frac{1-\cos x}{x}$ is:If $f(x)=x^2+3x$, then $f'(x)$ equals:The derivative of $\cos x$ with respect to $x$ is:The value of $\displaystyle\lim_{x\to 3}\frac{x^2-9}{x-3}$ is:For a constant $c$, $\dfrac{d}{dx}\big(c\,f(x)\big)$ equals:The value of $\displaystyle\lim_{x\to 0}\frac{\tan x}{x}$ is:The limit $\lim_{x\to 2}(x^2 + 3x - 1)$ equals:The limit $\lim_{x\to 0} in x/x$ equals:The derivative of $f(x) = x^3 + 2x^2 + 1$ at $x = 1$ is:The derivative of $ in x$ is:If lim_{x→a} f(x) = L and lim_{x→a} g(x) = M (with M ≠ 0), then lim_{x→a} f(x)/g(x) equals: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: