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Unformatted text preview: lim x → 3 √ x + 12 x3 . 5. Evaluate the limit, if it exists (possibly as an inﬁnite limit). lim x → π/ 2 tan x 6. Evaluate the limit, if it exists (possibly as an inﬁnite limit). lim x →∞ tan1 ( x 2x 4 ) 7. In the deﬁnition of the limit lim x → 1 (53 x ) = 2 , ﬁnd a value of δ that works for ε = 0 . 1. 8. Prove that there is at least one real solution of the equation xe x = 1. 1 9. For what value of the constant c is the function f ( x ) = ± x + c if x ≤ 1 x 2c if x >1 continuous on (∞ , ∞ )? 10. Diﬀerentiate the function f ( x ) = ( √ x1)( e x + x ) 11. Diﬀerentiate the function f ( x ) = 1 x 3x + 2 12. Find an equation of the tangent line to the curve y = √ x at the point (4 , 2). 13. Diﬀerentiate e x (cos x + sin x ). 2...
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 Fall '08
 WILKENING
 Calculus, Derivative, Continuous function

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