MA103-Winter-2016-Mid-Solutions.pdf - MA103 Midterm Test Solutions Page 1 of 8 1 Find the following limits if they exist[4 marks[4 marks 3x ex x 4x 2x

# MA103-Winter-2016-Mid-Solutions.pdf - MA103 Midterm Test...

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MA103 – Midterm Test Solutions Page 1 of 8 1.Find the following limits, if they exist:(a)limx→∞3x-ex4x-2x[4 marks] (b) limx0tan(3x)[4 marks] (c) limx0xsinx[4 marks]
MA103 – Midterm Test Solutions Page 2 of 8 2.Suppose thatf(x) is a continuous function and|f(x)-3 cosx|< x2forx6= 0 near 0. Find[5 marks]f(0). 3.Find the derivative off(x) =x2-3 atx= 2 using the limit definition of derivatives.[4 marks](Note:Youcannotuse L’Hospital’s rule.)
MA103 – Midterm Test Solutions Page 3 of 8 4.Consider the equation 2 sin-1x+ex= 0.(a) Show that it has a solution in the interval (-1,1).[4 marks]