1. Find the values of a, b and c so that the curve y=ax^2+bx+c passes through the point (0,4) and such that the tangent to the curve at the point (1,2) is parallel to teh line y=x+1.
2. (Related Rates Question). Two sides of a triangle are 2m and 3m in length and teh angle between them is increasing at a rate of 4 rad/min. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is pi/6.
3. (Hyperbolic Function Limit). Find limit as x-->0.
(sinhx)/(e^x)
4. Let f(x)=
-x+2 x≤1
x^2-2x+2 x>1
Is f differentiable at 1? Justify answer by using definition of differentiability at a point (Not supposed to do any derivates).
Don't just want the answers, actually want to learn how to do them.
+Rep .