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Hits: 5 Question An increasing function, , is defined for x > n, where n is an integer. It is given that . Find the least possible value of n. Solution We are given derivative of the function as; We are also given that it is an increasing function. To test whether a function is […]
Hits: 6 Question The coordinates of two points A and B are (1, 3) and (9, −1) respectively and D is the mid-point of AB. A point C has coordinates (x, y), where x and y are variables. i.State the coordinates of D. ii.It is given that CD2 = 20. Write down an equation relating […]
Hits: 220 Question The function f is defined by for . i. Express in the form of . ii. Hence find the set of values of for which , giving your answer in exact form. Solution i. We have the expression; We use method of “completing square” to obtain the desired form. We complete […]
Hits: 350 Question The curve C1 has equation y = x2− 4x + 7. The curve C2 has equation y2 = 4x + k, where k is a constant. The tangent to C1 at the point where x = 3 is also the tangent to C2 at the point P. Find the value of k […]
Hits: 327 Question The function f is defined by for . i. Express in the form of where and are constants. ii. State the greatest value of . The function g is defined by for . iii. Find the value of for which . Solution i. We have the expression; […]
Hits: 300 Question The line , where is a constant, is a tangent to the curve at the point on the curve. i.Find the value of . ii.Find the coordinates of . Solution i. We are given equation of the line as; We are given equation of the curve as; It is given that line […]
Hits: 221 Question i. Express in the form of . The function f is defined by for , where is constant. ii. State the largest value of for which is a decreasing function. The value of is now given to be 1. iii. Find an expression for and state the domain of . […]
Hits: 182 Question Two vectors, and , are such that and Where is a constant. i. Find the values of for which is perpendicular to . ii. Find the angle between and when q = 0. Solution i. We are given that; If and & , then and are perpendicular. Therefore, if […]