iCoachMath.com: Examples on Product and Quotient Rules of Limits - Limits and Their Properties

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e Find limx→3 [f(x) g(x)], if f(x) = 4x + 5 and g(x) = 5x + 4. e

e Find limx→5 [f(x) g(x)], if f(x) = 5x + 4 and g(x) = 2x² + 3. e

e Evaluate limx→2 [(2x² - 3)(4x² + 3)]. e

e Evaluate limx→3 [(6x + 4)(4x + 3)(3x + 2)]. e

e Find limx→2 [f(x) g(x) h(x)], if f(x) = x³ + 9, g(x) = x² + 2 and h(x) = x + 3.
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e Given f(x) = ax + b, g(x) = x - 6 and h(x) = 8 - x. If limx→3 [f(x) g(x)] = - 3 and limx→ - 3 [f(x) h(x)] = 3, then find the value of b.
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e Given f(x) = x + 6, g(x) = x + 2, limx→2 f(x) = l and limx→3 g(x) = m. Evaluate limx→6 (l f(x + g(x) f(x) + m g(x). e

e Evaluate limx→3 [(x² + 4x + 3)(x² + 3x + 4)]. e

e Evaluate limx→m (lx² + m) (mx² - l), if l, m are the solutions of the equation x² - 19x + 90 = 0 and l > m.
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e If limx→2 [x (x + 1) (x + 2) . . . . . . . . (x + 50)] = l, then which of the following statements is false? e

e Evaluate: limx→2 1(x + 8) e

e Evaluate: limx→2 (4x+2x) e

e Evaluate: limx→5 (x2+4x+1154x)
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e Evaluate: limx→2 (4xx+2) e

e Evaluate: limx→1 [1-x2+x3- . . . . .  -x261+x2+x3+  . . . . . +x26] e

e Evaluate limx→l (lx + 4lx + 3), if f(x) = 22 - 4x2x + 3 and limx→2 f(x) = l. e

e Which of the following is true, if f (x) = x² - 121, g(x) = x - 11?
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e f(x) = x - 1, g(x) = x³ - 1, then choose the correct statement from the folowing.
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e Find limx→5 [3f(x) + 2][5g(x) + 4], if limx→5 f(x) = 5 and limx→5 g(x) = 6.
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e If limx→3 (x+172x-2) = l, limx→2 (4x-133-x) = m, then write the quadratic equation whose roots are l, m.
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