Math Problem Solver

Question 1: (CLO2) (4)

Find the derivative of the following w.r.t 𝒙 using chain rule.

a) 𝑓(𝑥) = (1 + tan2 (𝑥

2 3 − 1)) 4

b) 𝑔(𝑡) = sin(𝑡2−1 𝑡2+1 )

Question2: (CLO2) (3)

Find the tangent of the equation 𝑦3 + cos(𝑥𝑦) = 𝑥2 at the point 𝑃(1,0).

Question3: (CLO1) (3)

a) Find lim 𝑦→0

sin(3𝑦). cot (5𝑦) 𝑦. cot (4𝑦) .

b) Find the values of 𝑎 and 𝑏 that make continuous everywhere.

𝑓(𝑥) ={ 𝑥2 − 4\ 𝑥 − 2, 𝑖𝑓 𝑥 < 2

𝑎𝑥2 − 𝑏𝑥 + 3, 𝑖𝑓 2 ≤ 𝑥 < 3

2𝑥 − 𝑎 + 𝑏, 𝑖𝑓 𝑥 ≥ 3 }