Question B3. [20 marks] a) Two sides of a triangle are 40 cm and 50 can in length and the angle between them is decreasi

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Question B3 20 Marks A Two Sides Of A Triangle Are 40 Cm And 50 Can In Length And The Angle Between Them Is Decreasi 1 (35.69 KiB) Viewed 8 times

Question B3. [20 marks] a) Two sides of a triangle are 40 cm and 50 can in length and the angle between them is decreasing at rate of 0.5°/s. Find the rate at which the area of the triangle is changing when the angle between the sides of fixed length is fr. (5) b) Iff is continuous on R and f(x)dx= -2². Find sin(2x=) f(sin³ (=z))dz. e) Evaluate the integral. (₁ tan³0 cos do END (5) d) Two cars start moving from the same point. One travels north at 120km/h and the other travels west at 50km/h. At what rate in km/h is the distance between the cars increasing? (5) Question B4. [20 marks] a) If a and b are distinct positive numbers, find the maximum value of f(z) = (-x)(1+z), where -1≤z≤0. 3 (5) ( b) Consider the function f(z) = cos 3z. (i) Show that there exists 0 <<3 such that f(f)=0. [5] (ii) By using a calculator, find an interval of length 0.1 that contains the you obtained in (1) above. (4) [6] e) Show that the function f(x)= has three points of inflection. [5]