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M 408C - Practice Final

M 408C - Practice Final - Practice Final Problems 1 Limits...

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Math 408C Practice Final Problems 1 Limits Evaluate the following limits. 1. lim x π 2 x 2 - π 4 x - π 2. lim x π - | x - π | x - π 3. lim x π + | x - π | x - π 4. lim x π x 3 ( x - π ) 5 5. lim x 0 sin( πx ) x 6. lim x →∞ sin( πx ) x 7. lim x →∞ x π - 3 8. lim x →∞ x π - 4 9. lim x →∞ πx 3 x 3 + x 2 + x + 1 10. lim x →-∞ cos( π x ) 1

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2 Differentiation 11. If d dx f ( x ) = 0, what can be said about f ( x )? Compute dy/dx for the following function using the limit definition of the derivative. 12. y = x 3 + x . Compute dy/dx for the following relations. 13. y = sec x ln x 14. y = π x x π 15. y = 1 /x 16. y = (tan x - sec x )(tan x + sec x ) 17. y = csc(sec x ) 18. y = e x ln x 19. y = tan( x ) tan - 1 ( x ) 20. y = sin - 1 ( x ) + sec - 1 (1 /x ) 21. y 2 + 2 y = sin x 22. y = x x 23. y 2 = x x 2
3 Applications of Differentiation Solve the following related rates problems. 24. Three children begin stretching out a large piece of latex in the shape of an equilateral triangle by each holding a corner as they walk away from its center (do not give children latex). If one of the sides is expanding at a rate of 1 m/s, how fast is the area expanding

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M 408C - Practice Final - Practice Final Problems 1 Limits...

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