MISC. EXERCISE Using differentials, find the approximate value of each of the following. (a) (b) Q.1 (a) Consider Then, Now, is approximately equal to and is given by, dy Δy Hence, the approximate value of = 0.667 + 0.010 = 0.677. (b) Consider. Let = 32 and = 1. x Δx Then, Now, is approximately equal to and is given by, dy Δy the approximate value of = 0.5 0.003 = 0.497. − Q.2 Show that the function given byhas maximum at = x e. Now, 1 log = 0 x − Q.3 The two equal sides of an isosceles triangle with fixed base are decreasing at the rate of 3 cm b per second. How fast is the area decreasing when the two equal sides are equal to the base?
MISC. EXERCISE Q.1 Using differentials, find the approximate value of each of the following. (a) (b) (a) Consider Then, Now, dy is approximately equal to Δy and is given by, Hence, the approximate value of = 0.667 + 0.010 = 0.677. (b) Consider. Let x = 32 and Δx = 1. Then, Now, dy is approximately equal to Δy and is given by, the approximate value of = 0.5 − 0.003 = 0.497. Q.2 Show that the function given byhas maximum at x = e. Now, 1 − log x = 0 Q.3 The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base?
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