Exams › JEE Main › Maths

If f(x) = ∑(n=0 to ∞) xⁿ/n! (log a)ⁿ, then at x = 0, f(x)

1. has no limit
2. is not continuous
3. is continuous but not differentiable
4. is differentiable

Correct answer: is differentiable

Solution

Sum x^n (log a)^n / n! = e^{x log a} = a^x, which is differentiable for all x (in particular at x=0). So f is differentiable.

Related JEE Main Maths questions

• Evaluate the limit as x approaches 0: ((1+tan x)/(1+sin x))^(csc x).
• Evaluate the limit as x approaches 0 of sin([x−3]) divided by [x−3], where [.] denotes the greatest integer function.
• Evaluate the limit as x approaches 0: (sin(x⁴) − x⁴ cos(x⁴) + x²⁰) / (x⁴(e^(2x⁴) − 1 − 2x⁴)).
• Evaluate the limit lim_(n→∞)(n³-8)/(n³+8). What is its value?
• If lim_(x→∞) (1+(λ)/(x)+(μ)/(x²))^(2x)=e², which of the following values of λ and μ is correct?
• Consider the following statements: Statement 1: If lim_(x→α)(sin(f(x)))/(x-α), where f(x)=ax²+bx+c, exists as a finite nonzero number, then lim_(x→α)(1/f(x)-1)/(1/f(x)+1) does not exist. Statement 2: The limit lim_(x→α)(sin(f(x)))/(x-α) can be finite only in the indeterminate form 0/0.

⚔️ Practice JEE Main Maths free + battle 1v1 →