1 10. Letf(x) = x² +3 --- 1. Its derivative satisfies 1 2.03 + x2 +1 (x + 1)(2.2 - 2+1) f'(x) = 2x +1+ = 22 (a) Evaluate lim f(c) and lim f(). 100- 20+

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adieLv10

17 Apr 2022

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17 May 2018

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2. a) Sketch the graph of a function f(x) that satisfies all the below conditions: 1- 0 1+0+ i) lim f() = 2 and lim f(0) = -1 and f(0) = -1 ii) lim f(x) = 3 and f(x) is discontinuous at x = 2 iii) lim f(x) = 0 and f(-3) = 2 2 +2 y=f(x) (7 marks) + N

2. a) Sketch the graph of a function f(x) that satisfies all the below conditions: f(x) = 1 and lim f(x) = -1 and f(0) = 1 X>07 i) lim X0 ii) lim f(x) = 3 and f(x) is discontinuous at x = -1 iii) lim f(1) = 0 and f(3) = 2 X- 3 (7 marks) y=f(x) • →X ya answers may vary.

f(1) [3] 8. Let f(x) = 2x2 +3.r. Use the definition of the derivative to prove that f'(x) = 4x+3. Solution: We have f(x) - f(a) 2,c2 + 3.r - 2a? - 3a 1+ I -a 1 r - a - lim 2(x + a)(x - a) + 3(x -a) -a = lim 2(+ a) +3 = 4a +3 = lim a 1-a - as required.

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1 10. Letf(x) = x² +3 --- 1. Its derivative satisfies 1 2.03 + x2 +1 (x + 1)(2.2 - 2+1) f'(x) = 2x +1+ = 22 (a) Evaluate lim f(c) and lim f(). 100- 20+

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