Hits: 43
Hits: 43 Question i. Find ii. Without using a calculator, find the exact value of giving your answer in the form , where a and b are integers. Solution i. We are required to find; provided that Rule for integration of is: We integrate both parts and […]
Hits: 28 Question The equation of a curve is . At the point on the curve with positive x-coordinate p, the gradient of the curve is . i. Show that . ii. Show by calculation that 2 < p < 3. iii. Use an iterative formula based on the equation […]
Hits: 40 Question A curve is defined by the parametric equations for . i. Show that . ii. Find the coordinates of the stationary point. iii. Find the gradientof the curve at point . Solution i. We are required to show that for the parametric equations given below; If […]
Hits: 45 Question Given that 3ex +8e−x = 14, find the possible values of ex and hence solve the equation 3ex +8e−x = 14 correct to 3 significant figures. Solution We are given; Let ; Now we have two options. Since ; Taking logarithm of both sides; and are inverse functions. The composite function is […]
Hits: 45 Question Solve the equation for . Solution We are given; except where or undefined Now we have two options. Using calculator; Now we find all solutions in the interval . Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of to find other solutions (roots) of : Therefore; […]
Hits: 47 Question Find the gradient of the curve at the point for which x = 0. Solution Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: We are given that; Therefore; Rule for differentiation of is: Rule for differentiation of natural exponential […]
Hits: 165 Question The polynomial is defined by i. Find the quotient when is divided by , and show that the remainder is 5. ii. Hence factorise completly. Solution i. Hence quotient is and remainder is . ii. We are required to factorise; When a polynomial, […]