(1) (a) (5 points) Find the derivative of, (i) f(x) = ln(ex + 3x) (ii) f(x)...

 

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(1) (a) (5 points) Find the derivative of, (i) f(x) = ln(ex + 3x) (ii) f(x) = e-3x3+x+5 (b) (5 points) Evaluate the following limits. If you are using a Theorem, please name it. (i) lim x+0 2e In (x+1)-2 (3x + e2x-1) I +22 (ii) lim 74 8r 1 - (2) (10 points) Evaluate the following integrals. 6x2 +12x (a) S dx (x3+3x+1) 1 (b) dx x(2-In x)2 (c) S 1e2x+1 dx e2x+2x giuon by (1) (a) (5 points) Find the derivative of, (i) f(x) = ln(ex + 3x) (ii) f(x) = e-3x3+x+5 (b) (5 points) Evaluate the following limits. If you are using a Theorem, please name it. (i) lim x+0 2e In (x+1)-2 (3x + e2x-1) I +22 (ii) lim 74 8r 1 - (2) (10 points) Evaluate the following integrals. 6x2 +12x (a) S dx (x3+3x+1) 1 (b) dx x(2-In x)2 (c) S 1e2x+1 dx e2x+2x giuon by