﻿ The left hand derivative of f (x) = [x] sin (πx) at x = k, k is an integer, is: : Kaysons Education

# The Left Hand Derivative Of f (x) = [x] Sin (πx) At x = k, k is An Integer, Is:

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## Question

### Solution

Correct option is

(–1)k (k – 1)π

If x is just less than k, [x] = k – 1

Now, LHD at x = k,

#### SIMILAR QUESTIONS

Q1

Let y = (x) be defined parametrically as y = t2 + t |t|x = 2t – |t|t Ïµ R Then at x = 0, find (x) and discuss continuity.

Q2

for what value of kf (x) is continuous at x = 0?

Q3

Determine a and b such that f (x) is continuous at x = 0.

Q4

Find the points of discontinuity of

Q5

Determine the form of g(x) = f ( f (x)) and hence find the point of discontinuity if g, if any.

Q6

Which of the following functions is differentiable at x = 0?

Q7

Let f (x) = [n + p sin x], x Ïµ (0, π), n Ïµ Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f (x) is not Differential.

Q8

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Q9

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

Q10

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | | ) is not differentiable at