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Hits: 125 Question a. Find b. Find the exact value of Show all necessary working. Solution a. We are given that; Rule for integration of is: Rule for integration of is: Rule for integration of is: b. We are required to find the exact value of; Rule for integration of is: Rule for […]
Hits: 42 Question Find the exact value of Solution We are given that; Rule for integration of is: Rule for integration of , or ; Rule for integration of is:
Hits: 29 Question Find the exact value of Solution We are given that; Rule for integration of is: Rule for integration of , or ; Rule for integration of is:
Hits: 81 Question a. Show that b. Find Solution a. We are required to show; Rule for integration of is: Rule for integration of is: Division Rule; Power Rule; Multiplication Rule; b. We are required to find; provided that provided that Rule for integration of is: Rule for integration of is: […]
Hits: 25 Question Show that Solution We are required to show; Rule for integration of is: Division Rule; Power Rule;
Hits: 65 Question Show that Solution We are required to show; Rule for integration of is: Division Rule; Power Rule;
Hits: 42 Question It is given that where a is a positive constant. i. Show that ii. Use the equation in part (i) to show by calculation that 1.5 < a < 1.6. iii. Use an iterative formula based on the equation in part (i) to find the value of a correct to […]
Hits: 80 Question It is given that where a is a positive constant. i. Show that ii. Use the equation in part (i) to show by calculation that 1.5 < a < 1.6. iii. Use an iterative formula based on the equation in part (i) to find the value of a correct […]
Hits: 56 Question Without using a calculator, find the exact value of Solution i. We are given that; Rule for integration of is: Rule for integration of , or ; Rule for integration of is:
Hits: 80 Question It is given that a is a positive constant such that i. Show that ii. Use the equation in part (i) to show by calculation that 1.0 < a < 1.5. iii. Use an iterative formula based on the equation in part (i) to find the value of […]
Hits: 65 Question i. Use the trapezium rule with four intervals to find an approximation to giving your answer correct to 3 significant figures. ii. Hence find an approximation to Solution i. We are required to apply Trapezium Rule to evaluate; The trapezium rule with intervals states that; We are given that […]
Hits: 38 Question It is given that a is a positive constant such that i. Show that ii. Use an iterative formula based on the equation in part (i) to find the value of a correct to 4 significant figures. Give the result of each iteration to 6 significant figures. Solution i. […]
Hits: 35 Question Given that find the value of the constant a correct to 3 decimal places. Solution i. We are given that; Rule for integration of , or ; Taking logarithm of both sides; for any
Hits: 58 Question Given that find the value of the constant a correct to 3 significant figures. Solution We are given that; Rule for integration of , or ; Taking logarithm of both sides; for any
Hits: 46 Question The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and the lines x = 0, x = 6 and y = 0 is denoted by R. i. Use the trapezium rule with 2 strips to find an estimate of the area of R, […]
Hits: 45 Question The definite integral is defined by i. Show that . ii. Sketch the curve for . iii. State whether an estimate of obtained by using the trapezium rule will be more than or less than 8e −2. Justify your answer. Solution i. We are given that; Rule […]
Hits: 42 Question i. It is given that the positive constant a is such that ii. Show that iii. Use an iterative formula , to find a correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution i. We are given that; Rule for […]
Hits: 48 Question a) Find b) Without using a calculator, find the exact value of giving your answer in the form . c) The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and the lines x = 0, x = 6 and y = 0 […]
Hits: 66 Question a) Find b) Without using a calculator, find the exact value of giving your answer in the form . c) The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and the lines x = 0, x = 6 and y = 0 is […]
Hits: 65 Question It is given that i. Show that ii. Use an iterative formula based on the equation in part (i) to find the value of a correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution i. We are given that; Rule for […]