MAT Review for Calc Unit 1

Use the graph of f(x) below to find the following limit. -1 0 1 dne lim x→1 f(x) = Use the graph of f(x) below to find the following limit. -1 0 1 dne lim x→1 f(x) = Use the graph of f(x) below to find the following limit. -1 0 1 dne lim x→1 f(x) = Use the graph of f(x) below to find the following limit. 0 +∞ -∞ dne lim x→4 f(x) = Use the graph of f(x) below to find the following limit. 0 +∞ -∞ dne lim x→3 f(x) = Identify the type of discontinuity and where it occurs for the following function. jump at x = 3 point at x = 3 infinite at x = 3 continuous f(x) = 4 x - 3 Identify the type of discontinuity and where it occurs for the following function. jump at x = -2 point at x = -2 infinite at x = -2 continuous f(x) = 3x + 6 Identify the type of discontinuity and where it occurs for the following function. infinite at x = 3, point at x = 2 infinite at x = 2, point at x = 3 infinite at x = 3, infinite at x = 2 point at x = 2, point at x = 3 f(x) = x - 2 x ^{2} - 5x + 6Identify the type of discontinuity and where it occurs for the following function. cont. when x ≤ -5/3 cont. when x ≥ -5/3 cont. when x = -5/3 continuous f(x) = √3x + 5 Identify the type of discontinuity and where it occurs for the following function. cont. when x ≤ 7/4 cont. when x ≥ 7/4 cont. when x = 7/4 continuous f(x) = √4x - 7 3 Find the average rate of change over the given interval. f(x) = 4x - 5 [2, 4] 1/4 3 4 12 Find the average rate of change over the given interval. f(x) = 3x ^{2} - 2x +1 [-2, 3]-5 -1 1 5 Find the limit h→0 of the average rate of change of f(x) = x 6 8 10 19 Find the slope of the line tangent to the curve f(x) = x 3 6 8 10 Find the limit of the following problem. -7 +∞ -∞ does not exist lim x→-3 x + 3 x - 4 Find the limit of the following problem. x→-2 ^{+}lim -5 5 +∞ does not exist (x + 7) x + 2 x + 2 Find the limit of the following problem. x→3 ^{-}lim -22 -8 8 9 { 2x + 3 if x ≥ 3 5x - 7 if x ≤ 3 Find the equation of the line tangent to the curve. y - 3 = 12(x - 7) y - 3 = 4(x - 7) y - 7 = 12(x - 3) y - 7 = 4(x - 3) f(x) = 4x + 9 at (3, 7) Find the equation of the line normal to the curve. y - 4 = 7(x - 2) y - 4 = -7(x - 2) y - 4 = 1/7(x - 2) y - 4 = -1/7(x - 2) f(x) = 3x ^{2} - 5x at (2, 4)Find the equation of the line tangent to the curve. y + 1 = 11(x - 2) y + 1 = -13(x - 2) y - 1 = 11(x + 2) y - 1 = -13(x + 2) f(x) = x ^{3} - x + 5 at (-2, 1) |

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