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# Ask a Continuity and Differentiability Question

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N

Nalini 10/11/2016 in  Continuity and Differentiability

Define differentiability?

0 0 3

Hussam Uddin replied | 22/11/2016

Differential means derivative has a unique value at that point. If a curve is smooth it has only one differential value and it is called differential.

Sarvajeet replied | 07/12/2016

df/dx= lim f(x+h)-f(x)/ h at h->0.

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M

Manu 10/11/2016 in  Continuity and Differentiability

What is the formula of derivative of sin inverse x?

D Chandra replied | 30/11/2016

d/dx(sin^-1)=1/(root(1-x^2))

Sarvajeet replied | 03/12/2016

1/square root (1-square of x).

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S

Sumit 10/11/2016 in  Continuity and Differentiability

What is the derivative of log x?

P

Prabha replied | 11/12/2016

1/x.

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D

Dr. 10/11/2016 in  Continuity and Differentiability

What do you mean by L. H. L and R. H. L?

Sourabh Sharma replied | 06/12/2016

Left and Right Hand Limit

Sarvajeet replied | 07/12/2016

Left and Right Hand Limit.

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S

Santosh 10/11/2016 in  Continuity and Differentiability

Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm?

Sarvajeet replied | 07/12/2016

41.4 cm.

Prassan replied | 08/12/2016

Suppose A is area of circle.A=piXr2
dA/dr=2XpiXr.
=2XpiX5
=2X3.14X5
=31.4. (Ans)

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R

Rajendra 10/11/2016 in  Continuity and Differentiability

The volume of a cube is increasing at the rate of 8 cubic cm/sec. How fast is the surface area increasing when the length of an edge is 12 cm?

Sarvajeet replied | 02/12/2016

(8/3) square cm/sec or 2.6667 square cm/sec.

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V

Vinodha 10/11/2016 in  Continuity and Differentiability

An edge of a variable cube is increasing at the rate of 3 cm per second. How fast is the volume of the cube increasing when the edge if 10 cm long?

Sarvajeet replied | 07/12/2016

900 cube cm per second.

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M

Mahender 10/11/2016 in  Continuity and Differentiability

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of its circumference?

Sarvajeet replied | 07/12/2016

4.4 cm/s.

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A

Ankit 10/11/2016 in  Continuity and Differentiability

A balloon, which always remains spherical has a variables radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm?

Sarvajeet replied | 26/11/2016

1257.14 cube cm/cm=1257.14 square cm

Tapas replied | 04/12/2016

Please see the attachment.

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A

Ankit 10/11/2016 in  Continuity and Differentiability

Differentiate the equation with respect to x: (square of x) + (square of y) = 25?

Sarvajeet replied | 02/12/2016

Differentiation of the equation with respect to x = -x/y.

Tapas replied | 04/12/2016

The given equation: x^2 + y^2 = 25.
Differentiating with respect to x:
2x + 2y(dy/dx) = 0
=> dy/dx = - 2x/2y = - x/y.

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A

Abinaya 10/11/2016 in  Continuity and Differentiability

The radius of an air bubble is increasing at the rate of 1 / 2 cm per second. At what rate is the volume of the bubble increasing when the radius is 1?

Sarvajeet replied | 26/11/2016

6.289 cube cm/sec

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A

Aishwarya 10/11/2016 in  Continuity and Differentiability

A balloon which always remains spherical, has a variable diameter 3 / 2 (2x + 1). Find the rate of change of its volume with respect to x?

Sarvajeet replied | 02/12/2016

-((27.pie)/8) ((2x+1) power(-4)).

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Y

Yusufali 10/11/2016 in  Continuity and Differentiability

Determine the continuity of the function: f(x) = sin x + cos x?

Hussam Uddin replied | 22/11/2016

f(x) = sin x - sin (x+ 90), 2 sin (x + 45 ). sin (-45) = -2/sin 45.
sin (x+45) = constant.
sin (x+45 ) which is a continuous function for all values of x.

Siva Naga Raju replied | 22/11/2016

Both sin x and cos x are continuous functions.
The sum or difference of continuous functions is also a continuous function.
Alternate way is multiply and divide the equation by sqrt (2), sin x + cos x can be written as sqrt (2) * sin(x+45).

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M

Maliha 10/11/2016 in  Continuity and Differentiability

Determine the continuity of cosine x?

A

Anjali replied | 23/11/2016

It is evident that as h approaches 0, the coordinate of P approach the corresponding coordinate of B.
But by definition we know,
sin(0) = 0 and cos(0) = 1
The values of the functions match with those of the limits as x goes to 0 (Remind the definition of continuity we have).
limx tends to 0 sin(x) = sin(0) = 0 limx tends to 0 cos(x) = cos(0) = 1

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A

Amit 10/11/2016 in  Continuity and Differentiability

What do you mean by the function is strictly increasing and decreasing with respect to continuity?

Rama Krishna replied | 08/12/2016

Dear Student,
Increasing Functions:
A function is "increasing" when the y-value increases as the x-value increases.
Decreasing Functions:
The y-value decreases as the x-value increases.

Ankit replied | 09/12/2016

At no point slope is zero. It is of same symbol throughout the domain.

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S

Selvi 10/11/2016 in  Continuity and Differentiability

Find the value of k: f(x) = kx; 3 if x < 2 at x = 2?

S

Srinivas replied | 25/11/2016

Let x--->2 kx=3
k*2=3
k=3/2.

Sarvajeet replied | 07/12/2016

kx=3
2k=3;
k=3/2;

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A

Asif 10/11/2016 in  Continuity and Differentiability

Find the value of k: f(x) = kx + 1; 3x - 5 if x < 5 at x = 5?

Ankit replied | 09/12/2016

9/5.

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M

Mukundan 10/11/2016 in  Continuity and Differentiability

A function f(x) is defined as:
f(x) = {x - 6 / x - 3; 5 if x = 3
Show that f(x) is continuous at x = 3?

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J

Jayashree 10/11/2016 in  Continuity and Differentiability

Find the value of a if the function f(x) is defined by: f(x) = 2x - 1; a, x=2; x + 1, x > 2?

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T

Tashiruddin 10/11/2016 in  Continuity and Differentiability

The total revenue in rupees received from the sale of x units of a product is given by: R(x) = 13x + 15. Find the marginal revenue when x = 7?

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H

Hemlata 10/11/2016 in  Continuity and Differentiability

Find the rate of change of the circle with respect to its radius r at r = 6 cm?

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A

Aditya 10/11/2016 in  Continuity and Differentiability

Solve the function with respect to x which is strictly increasing on R: f(x) = 3x + 17?

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A

Archit 10/11/2016 in  Continuity and Differentiability

Show that the function given by: f(x) = [(e) power 2x]?

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D

Dipak 10/11/2016 in  Continuity and Differentiability

Find the intervals in which the function f given by f(x) = 2x - 3 which is strictly increasing?

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K

K. 10/11/2016 in  Continuity and Differentiability

Find all the points of discontinuity of f, where f(x) = sin x / x; x + 1 if x = 0 and x < 0?

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