tan applied calculus solutions

Put t = tan - 1 x or x = tan t when x = 0 tan t = 0 when x = 1, tan t =1 ..

Let y = f (x) = x 1 / 4 Let x = 81, d x =1. Taking these values we have ..

f (x) = x 3 - 6x 2 + 9x + 15 f ' (x) = 3x 2 -12x + 9 = 3(x 2 - 4x + 3) = 3 (x - 1) (x - 3) Thus x = 1 and x = 3 are the only points which could be the points of local maxima or local minima. Let us examine for x=1 When x<1 (slightly less than 1) f '(x) = 3 (x - 1) (x - 3) = (+ ve) (- ve)..

Since the tangent to the given curve is parallel to the line 4x - 2y + 5 = 0 Slope of the tangent = Slope of the given line On simplification, the equation is 48 x - 24y = 2..

We are given that a = 0, b = 4 or nh = 4 By definition, ..

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Let m 0 be the moisture content initially and let m be the moisture content after t hours. According to problem: when t = 0, m= m 0 log m = kt + log m 0 Substituting in (2), we have \ Equation (2) becomes (i) Again when the sheet losses 95% of the moisture, m = Equation ..

Let the initial population be P 0 and P be the population of the colony at any instant t. Then according to the problem when t = 0, P= P 0 Equation (1) becomes log P = kt + log P 0 .(2) when P 0 is doubled, P = 2P 0 where t = 50 days From equation (2) log (2 P 0 ) = 50 k + log P 0 ..

If we replace y by , we have y'+ y \ f (x) satisfies the equation y' + y = 2 Moreover, ..

Let y = tan - 1 x. Then tan y = x. Differentiating both sides w.r.t. x, we get ..