1 . Solve for x: (a) x2 - x = logs /25 (b) log1. [10.1 = x (c) (1 +0.09)12x 12 ) *= 3 (d) 23-x = 625 (e) log, [x3 = 1.9 2. Find the derivative of the following functions. (a) y = 5-4x (b). y = -7x(8-2x) (c). h(0) = 2-0 cosne (d). f(x) = 10g2 x-1 (e) g(x) = 1085 (x2. V1-x 3 . Find the equation of the tangent line to the graph of the funtion at the given point. (a) y = 2-x, at point (-1, 2) (b). y = log3 x, at the point (27, 3) 4. Use the logarithmic differentiation to find dy (a). y = x2/x (b). y = (x-2)*+1 5. Find the indefinite integral. (a) S( x2 + 2-* ) dx ( b). S x (5 -x2) dx (c). S 32 x 1+32x dx 6. Evaluate the definite integral. (a) [ 3*/4 dx ( b ) . S ( 4 * + 1 + 2 * ) dx 7. Find the area of the region bounded by the graph of the equation y = 3cos x sin x , y = 0, x = 0, x = n 8. Evaluate the limit using L'Hopital's Rule. (a). lim V25-x2 (b). lim In x (c). lim x sin = (d). lim i In(ett-1)at x-0 x - 5 x-1 sinnx n - co n -too x e). lim sin 5x (f) lim (ex + x)x(g). lim (3 (h) lim (ex - x) x-0 tan 9x x-1+ Inx x - 1/ n - ooWorksheet 1 1 . Solve for x: (a) x2 - x = logs 25 (b) log10 0.1 = x (c) (1 4 0.09)12x 12 = 3 (d) 23-x= 625 (e) log7 [x3 = 1.9 2 . Find the derivative of the following functions. (a) y = 5-4x (b). y = -7x(8-2x) (c). h(0) = 2-0 cosne (d). f(x) = 10gz x_ x2 4 (e) g(x) = 1085 x2 .V1-x