मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता १२

If the volume of a cube of side length x is v = x3. Find the rate of change of the volume with respect to x when x = 5 units - Mathematics

Advertisements
Advertisements

प्रश्न

If the volume of a cube of side length x is v = x3. Find the rate of change of the volume with respect to x when x = 5 units

बेरीज

उत्तर

Volume of a cube v = x3

Rate of change dvdx = 3x2

When x = 5 units

dvdx = 3(5)2

= 3(25)

= 75 units

shaalaa.com
Meaning of Derivatives
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Applications of Differential Calculus - Exercise 7.1 [पृष्ठ ८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 7 Applications of Differential Calculus
Exercise 7.1 | Q 4 | पृष्ठ ८

संबंधित प्रश्‍न

A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres. Find the average velocity between t = 3 and t = 6 seconds


A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres. Find the instantaneous velocities at t = 3 and t = 6 seconds


A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t2 in t seconds. How long does the camera fall before it hits the ground?


A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. At what times the particle changes direction?


A stone is dropped into a pond causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate at 2 cm per second. When the radius is 5 cm find the rate of changing of the total area of the disturbed water?


Find the slope of the tangent to the following curves at the respective given points.

y = x4 + 2x2 – x at x = 1


Find the slope of the tangent to the following curves at the respective given points.

x = a cos3t, y = b sin3t at t = π2


Find the point on the curve y = x2 – 5x + 4 at which the tangent is parallel to the line 3x + y = 7


Find the points on curve y = x3 – 6x2 + x + 3 where the normal is parallel to the line x + y = 1729


Find the points on the curve y2 – 4xy = x2 + 5 for which the tangent is horizontal


Find the tangent and normal to the following curves at the given points on the curve

y = x2 – x4 at (1, 0)


Find the equations of the tangents to the curve y = -x+1x-1 which are parallel to the line x + 2y = 6


Choose the correct alternative:

The volume of a sphere is increasing in volume at the rate of 3π cm3/ sec. The rate of change of its radius when radius is 12 cm


Choose the correct alternative:

A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. The rate of change of the balloon’s angle of elevation in radian per second when the balloon is 30 metres above the ground


Choose the correct alternative:

The position of a particle moving along a horizontal line of any time t is given by s(t) = 3t2 – 2t – 8. The time at which the particle is at rest is


Choose the correct alternative:

The abscissa of the point on the curve f(x) = 8-2x at which the slope of the tangent is – 0.25?


Choose the correct alternative:

The slope of the line normal to the curve f(x) = 2 cos 4x at x = π12 is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.