Calculus I - Problems for Test II | MTH 125S, Exams of Calculus

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Mth 125s Practice Problems for Test 2 Please show all work neatly and completely using proper technique and notation in the space provided as discussed in class. 1. Compute the derivative of each function. (a) Esa? -245 + 4e? — Se +10) (6) Lfasinx + 7c0sx + 9tanz] (c) £18 seox + 2cscx + 5cotx] (@) 4 [er + ing] (e) Lirsin tz + Scos'x + 4tan“!x] (p £[N3 sec“tx + llesc!x + 9cot™ x] (@) (2° + log] () StS +E] 2. Compute the derivative of each function. (a) 4. [428 sin2x] ) £2] (c) L110? +4x41)2] @ LlnGxt + 4x)] (e) Lian] ) Zere"] (g) Lox" cos?x + 6x4 sin?x] (h) ZL foot!3xtan'3x + 7x? sec? — Tx? tan?) d 3. Use logarithmic differentiation to compute es for each of the following functions and simplify the expression completely: (a) 20 {G74 3(x - 2)? + 2)* 4. Use implicit differentiation to compute # for each of the following functions and simplify the expression completely: (a) xy3 +x? = y4, (b) x? + y? = x, and (c) sin@zy) = x-y. pel =, (b)x3(x? + 1)" = y*, and (ce) = 5. Compute each limit using L’Hopital’s rule when appropriate. (@) lim 28 —7x2 + 4xt1 x—1+Inx 2 yy? lim —3e2 +x (©) ims 12 + 6x — Se" (6) lim @— 1)Ingx~ 1) (d) lim (1 ~ 7x)3* a0" im tanc!x aE 6. Find the equation of the tangent line to each function at the given point (a) fx) = x° + 2x? + 10 at x = 2 and f(x) = 2Inx-2atx =e. 7. Compute the total differential and the increment in standard form for each function: (a) f(x) = 10x + 4 and (b) fx) = x? + 3x-4. inft+h)-1 2+ hyo — 8. Express each limit as a derivative and then evaluate: (a) Jim aE and (b)lim oe