Question

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se the properties of limits to help decide whether the limit exists. If the limit exists, find its value. 7) lim+12xs+27 x-+-9x+9 A) 216 B) 12 C) Does not existD)-6 ifferentiate. 8)f(x) =4x4-7x3-3 8) , A) f'(x) = 16x3-21x2-7 C) f(x) = 4x3 + 3x2 B) Px)-4x3 3x2-7 D) f(x) 16x3 -21x2 9) y (2 2 9) dy )4.6x5 + 20x3 + 24x B)-=6x5 + 24x3 + 24x c a24x3+24x = 6x5 +12x3 +12x D) dx 10) 10) y =x-3 dy 4 1 dx x2 3 dy 4 x dx x23 dx 11) 11) Find the slope of the graph of y 2x2.1 at the point (2,3). B) C) 12 E) none of these 12) 12) Find the first derivative of y T-9T5+2T4.59 A) T6-9T4+2T3 C) 7T6-45T+8T3 B) 7T6-45T4+8T3+59 D)T6-9T4 2T3 59

Answer 1

lim_x rightarrow -9 x^2 + 12 x + 27/x + 9 (0/0) form using L. Hospital Rule lim_x rightarrow -9 2x + 12/1 = 2 times (-9) + 12/1 = -18 + 12/1 = -6 [because D. w. r. t x Numerator and denominator] (D) is currect f(x) = 4x^4 - 7x^3 -3 f'(x) = 16x^3 - 21 x^2 [because d/dx (x^n) = nx^n - 1] (D) is current y = (x^2 + 2)^3 = > dy/dx = 3(x^2 + 2)^3 - 1 middot 2x = > dy/dx = 3(x^2 + 2)^2 middot 2x = 6x (x^2 + 2)^2 = 6x [x^4 + 4 + 4x^2] [(a + b)^2 = a^2 + b^2 + 2ab] dy/dx = 6x^5 + 24x + 24x^3 = > (B) is currect \r\n y = 4/x - x/3 = > dy/dx = d/dx (4/x - x/3) = d/dx (4/x) - d/dx (x/3) = 4 d/dx (1/x) - 1/3 d/dx (x) = 4 d/dx (x^-1) - 1/3 (1) = 4(-1 x^-1 -1) - 1/3 = 4(-1/x^2) - 1/3 dy/dx = -4/x^2 -1/3