1. The amount of water in a tank t minutes after it has started to drain is given by w = 100(t − 15)² gallons. The water is running out after 5 minutes at the rate of:
At a certain instant, the height of a cylinder is 6 in. and increasing at 1 in./s, while the radius is 2 in. and decreasing at 1 in./s. The rate of change of the volume is:
A particle is moving along the curve y = x ln x. Find all values of x at which the rate of change of y with respect to time is 3 times that of x (assuming dx/dt ≠ 0).
If y = 2x + 1 and Δy = 3, then Δx will be:
At what point does the function y = ln x/x attain its maximum value?
Find the extreme value(s) of the function f(x) = x³/3 − 2x² + 3x + 1, for all x ∈ ℝ.
If the radius of a circle is increased from 6 cm to 6.1 cm, find the approximate increase in the area.
Find dy/dx if x³y = 1 at the point (1, 1).
The distance covered by a body after time t is given by s = √(2t² + 1) Its velocity after 3 s is:
If s = log₁₀(t), where s is the distance covered by a body after time t, find its velocity after 2 seconds.
The angle of the tangent (with respect to the x-axis) drawn at the origin to the curve y(x² + 1) = x is:
The slope of the tangent to the curve x² + y² = 2 at the point where y(10) = 2 is:
Given the curve y = x³ − 3x² − 9x + 11 calculate the coordinates of its stationary points.
Find the point on the curve y = (x − 2)/(1 − x) at which the tangent is parallel to the line y = 5 − x.
The radius r (cm) of a circle is given by r = 9t − t³ where t is time in seconds. Find the rate of change of the radius at t = 2 s.
If y = 2eˣ + e⁻ˣ, the extreme value occurs at:
If f(x) = x³ − 9x² + 15x + 3, the relative maximum value is: (a) (b) 1 (c) (d) (e)
If f(x) = ln x/x, the extreme value is:
If f(x) = ln(1 + x²), the stationary point is:
If f(x) = ln(1 + x²), the stationary point is:
