Limits at Infinity Evaluate each of the following limits at infinity. 6 x3 lim - 4x...

 

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Limits at Infinity Evaluate each of the following limits at infinity. 6 x3 lim - 4x + 5 a) x+ o 4 x3 + 2 x2 + 1 { lim_(x-> infinity) [ (6x^3 - 4x + 5) / (4x^3+ 2x^2 +1)] } 2x + 1 b) lim 9x2 + 4 { lim_(x-> infinity) [ (2x + 1)/( sqrt(9x^2+4))] } ex - e-x c) lim x+ o e* + e-x QUESTION 30 curve sketching Sketching curve f(x) given by 1 f(x) x2 + 36 { f(x) = [ 1/ (x^2 + 36)] } a. First derivative and critical points to find regions where increasing and decreasing. Also classify critical points as relative maximum, relative minimum, or neither. b. Second derivative and its zeros to find regions where concave up and concave down. Identify inflection points. C. symmetry d. limit at infinty (and asymptotes) try sketching the graph QUESTION 31 4 optimization word problem Find the dimensions of the largest rectangle (in area) that can be inscribed in a semicircle of radius 5. The rectangle would have its base along the x-axis, and its height is determined by a point along the semicircle y = 25 x2 QUESTION 32 differentials Approximate the value of the following expression by using differentials and linear approximation 26.5 { cuberoot(26.5) } This is based on the function f(x) = x at a = 27. { f(x) = cuberoot(x) } at a = 27. Limits at Infinity Evaluate each of the following limits at infinity. 6 x3 lim - 4x + 5 a) x+ o 4 x3 + 2 x2 + 1 { lim_(x-> infinity) [ (6x^3 - 4x + 5) / (4x^3+ 2x^2 +1)] } 2x + 1 b) lim 9x2 + 4 { lim_(x-> infinity) [ (2x + 1)/( sqrt(9x^2+4))] } ex - e-x c) lim x+ o e* + e-x QUESTION 30 curve sketching Sketching curve f(x) given by 1 f(x) x2 + 36 { f(x) = [ 1/ (x^2 + 36)] } a. First derivative and critical points to find regions where increasing and decreasing. Also classify critical points as relative maximum, relative minimum, or neither. b. Second derivative and its zeros to find regions where concave up and concave down. Identify inflection points. C. symmetry d. limit at infinty (and asymptotes) try sketching the graph QUESTION 31 4 optimization word problem Find the dimensions of the largest rectangle (in area) that can be inscribed in a semicircle of radius 5. The rectangle would have its base along the x-axis, and its height is determined by a point along the semicircle y = 25 x2 QUESTION 32 differentials Approximate the value of the following expression by using differentials and linear approximation 26.5 { cuberoot(26.5) } This is based on the function f(x) = x at a = 27. { f(x) = cuberoot(x) } at a = 27.