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Hits: 251 Question i. By differentiating , show that if y = cot x then ii. By expressing in terms of and using the result of part (i), show that iii. Express cos 2x in terms of sin2 x and hence show that can be expressed as . Hence […]
Hits: 218 Question i. By sketching a suitable pair of graphs, show that the equation has only one root. ii. Verify, by calculation that this root lies between x=0 and x=0.5. iii. Show that, if a sequence of values given by the iterative formula converges, then it […]
Hits: 204 Question The equation of the curve is . i. Show that ii. Find the equation of the tangent to the curve at the point (1,2), giving your answer in the form ax+by=c. Solution i. We are given that; Therefore; Rule for differentiation of is: Rule for differentiation […]
Hits: 146 Question i. Show that the equation can be written in the form ii. Hence solve the equation for . Solution i. We are given; We apply following addition formula on left side of given equation. Therefore; Since; ii. We are required to […]
Hits: 132 Question Show that Solution We are required to show that; Rule for integration of is: This integral is valid only when . Division Rule; Power Rule;
Hits: 213 Question i. Given that y = 2x, show that the equation 2x + 3(2−x) = 4 can be written in the form y2 − 4y + 3 = 0. ii. Hence solve the equation 2x + 3(2−x) = 4 giving the values of x correct to 3 significant […]
Hits: 181 Question The polynomial is denoted by . i. Find the quotient and remainder when is divided by . ii. Use the factor theorem to show that is a factor of . Solution i. Hence quotient is and remainder is . ii. We are given that; […]
Hits: 169 Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the inequality; It can be written as; We have to consider two separate cases; When When Therefore the inequality will hold for ; SOLVING […]