Calculus

Question 1

Given the curve y = x³ + x² - x + 3. Find the slope at x =1.

Answer 1

y = 4

Question 2

Given the curve y = x³ + x² - x + 3. Find the tangent at x =1.

Answer 2

4x - y = 0

Question 3

Given the curve y = x³ + x² - x + 3. Find the normal at x =1.

Answer 3

x + 4y - 17 = 0

Question 4

Given the curve y = x³ + x² - x + 3. Find the subnormal at x =1.

Answer 4

S(sub N) = 16

Question 5

Find the function y = f(x) whose graph passes through the point (1, 2) that also satisfies dy/dx = 3x² - 3.

Answer 5

y = x³ - 3x + 4

Question 6

A circle is inscribed in a sector of radius 24 cm and central angle 60°. Compute the difference in areas between the sector and the inscribed circle.

Answer 6

22π cm²

Question 7

An open-topped rectangular box is to have a square cross-section and has a capacity of 12,000 cm³. Find the height of the box that requires the minimum amount of material in making it.

Answer 7

14.42 cm

Question 8

Find the max. area of the curve represented by x = 4 cos t and y = 3 sin t when 0 <= 1 <= 2π.

Answer 8

12π