1. Determine 2. At what point of the curve y=cosh x does the tangent have slope 1? 3. Find the value of the expression by interpreting.

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1. Determine 2. At what point of the curve y=cosh x does the tangent have slope 1? 3. Find the value of the expression by interpreting it as a definite integral of some function. Evaluate this integral by interpreting it as an area. 4. Evaluate the definite integral by interpreting it as an area. 5. f(x)=sec x on [π/6,π/3]. Write down expressions for L3, R3 , M3,. 6. Show that the equation has exactly one real root. 7. Find two positive numbers whose product is 100 and sum is minimal. 8. Find the area of largest rectangle that can be inscribed in a semicircle of radius r. 9. Find point on parabola y2=2x closest to the point (1,4). 10. If a and b are positive numbers, find the maximum value of HOMEWORK PROBLEMS!!! Problems solved in the class. Optimization problems (see lecture notes Week 3). Basic functions and their derivatives (see lecture notes Week 1).

FCT - connection between definite integral and antiderivative: New notation for antiderivative: Indefinite integral: - number! - function! (family of functions)

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F(x) represents rate of change of y=F(x) F(b)-F(a) net change in y when x changes from a to b. Net change Th. The integral of a rate of change is a net change: