1 markLimits
CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 2 · Question 5(b)
The function f on R is defined by f(x) = {x²+1, x>1; 4+px, x<1}.
Find
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- 5(a)(i)Find the values of x for which (x³+8)/(x²-4) is discontinuous.[2 marks]
- 5(a)(ii)Hence, or otherwise, find lim_{x→-2} (x³+8)/(x²-4).[3 marks]
- 5(a)(iii)By using the fact that lim_{x→0} (sin x)/x = 1, or otherwise, find, lim_{x→0} (2x²+4x)/(sin 2x).[5 marks]
- 5(b)(i)a)lim_{x→1+} f(x)[2 marks]
- 5(b)(i)b)the value of the constant p such that lim_{x→1} f(x) exists.[4 marks]
- 5(b)(ii)Hence, determine the value of f(1) for f to be continuous at the point x = 1.[1 mark]
- 5(c)find the values of u and v.[8 marks]
More practice: the rest of this paper · more Limits questions · all CAPE Pure Mathematics Unit 1 past papers