Assignment:
Q1. Write an equation of the line tangent to the curve y=f(x) at the given point P on the curve. Express the answer in the form ax+by=c.
1)y=3x^2-4; P(1,-1)
2)y=2x-1/x; P(0.5,-1)
Q2. Give the position function x=f(t) of a particle moving in a horizontal straight line. Find its location x when its velocity v is zero.
1)x=-16t^2=160t+25
Q3. Give the height y(t) (in feet at time t seconds) of a ball thrown vertically upward. Find the maximum height that the ball attains.
1)y=-16t^2+128t+25
Q4. Evaluate the Limits
1)lim as h goes to 0= 1/h(1/sqrt 9+h - 1/3)
2)lim x goes to 0= (sqrt 1+x - sqrt 1-x)/x
Q5. Find a slope-predictor function for the given function f(x). Then write an equation for the line tangent to the curve y=f(x) at the point where x=2.
1)f(x)=x/x+1
2)f(x)=x^2+3/x
3)f(x)=x^2/x+1
Provide complete and step by step solution for the question and show calculations and use formulas.