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Let a0, a1 ::: be the series recursively defined by a0 = 1, and an = 3 + an-1 for n ≥ 1.
(a) Compute a1, a2, a3 and a4.
(b) Compute a formula for an, n ≥ 0.
(c) Use induction to show that your formula is right.
Example of Trig Substitutions Evaluate the subsequent integral. ∫ √((25x 2 - 4) / x) (dx) Solution In this type of case the substitution u = 25x 2 - 4 will not wo
HE IGHTS AND DISTANCES If the angle of elevation of cloud from a point 'h' meters above a lake is α and the angle of depression of its reflection in the lake is β , prove
how to find x,y and z in parallelograms,rhombus etc.
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sin10+sin20+sin30+....+sin360=0 sin10+sin20+sin30+sin40+...sin180+sin(360-170)+......+sin(360-40)+sin(360-30)+sin(360-20)+sin360-10)+sin360 sin360-x=-sinx hence all terms cancel
Sherman took his pulse for 10 seconds and counted 11 beats. What is Sherman's pulse rate in beats per minute? A 10 second count is 1/6 of a minute. To find out the number of be
A golf ball has a diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the d
what are the advantages and disadvantages of both Laspeyres and Paasche index
A pipe has a diameter of 2.5 inches. Insulation which is 0.5 inches thick is placed around the pipe. What is the diameter of the pipe along with the insulation around it? The i
Example: Find a general solution to the subsequent differential equation. 2 y′′ + 18 y + 6 tan (3t) Solution First, as the formula for variation of parameters needs coe
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