MA103 Fall 2012 Midterm - 2012 Fall MA103 Midterm Test[4 marks Page 1 of 2 1 Find a formula for the inverse of the function f(x = 1 3 2x x 3\/2 Also

# MA103 Fall 2012 Midterm - 2012 Fall MA103 Midterm Test[4...

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MA103 – Midterm Test 2012 Fall Page 1 of 2 1. Find a formula for the inverse of the function[4 marks]f(x)=1+32x,x3/2.Also, determine the domain of the inverse function.2.(a) State the Intermediate Value Theorem.[3 marks] (b) Show that the functiong(x)=has a root in [1,0].[3 marks]3. If3x+2f(x)x2+3x+11,for allx0, findlimx→−3f(x).[3 marks]4. Let[4 marks]f(x)=braceleftbiggx2+K,x1,tan(π4x),x >1.Determine the value ofKthat makesfcontinuous atx= 1.5. Find the derivative ofy= 2xx2+3atx= 2by using the limit definition[5 marks]of derivative.6. Use logarithmic differentiation to find the derivative ofy=(sinx)1/x.[4 marks]7. Evaluatelimθ0tan(3θ)sin(4θ).[4 marks]8. Determine an equation of the line tangent tof(x)=xln(x2+1)atx=1.[3 marks]9.(a) Give a precise statement, in terms of epsilons and deltas, of the definition that[4 marks]the limit off(x) asxapproachesais L (i.e., limxaf(x) =L).(b) Determine a valueδ >0 such that for all0<|x3|< δthen|62x|<[3 marks]0.6.10.(a) Let