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4.4 - Indeterminate Forms and L’Hospital’s Rule

4.4 - Indeterminate Forms and L’Hospital’s Rule. L’Hospital’s Rule. Suppose f and g are differentiable functions and g '( x ) ≠ 0 near a (except possibly at a ). Suppose that or that Then if the limit on the right side exists (or is ±∞). L’Hospital’s Rule.

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4.4 - Indeterminate Forms and L’Hospital’s Rule

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  1. 4.4 - Indeterminate Forms and L’Hospital’s Rule

  2. L’Hospital’s Rule Suppose f and g are differentiable functions and g'(x) ≠ 0 near a (except possibly at a). Suppose that or that Then if the limit on the right side exists (or is ±∞).

  3. L’Hospital’s Rule In simpler terms, if after substituting in a, Then if the limit on the right side exists (or is ±∞).

  4. L’Hospital’s Rule if f(a) = f(b) = 0

  5. Indeterminate Forms 1. 0 / 0 or ±∞ / ±∞ Strategy: Apply L’Hospital’s Rule Directly 2. 0 · ±∞ Strategy: Apply L’Hospital’s Rule to

  6. Indeterminate Forms 3. ±∞ - ±∞ Strategy: Try factoring, rationalizing, finding common denominator, etc. to get into form 1 above. 4. 00 or ∞0 or 1∞ Strategy: Use a method similar to logarithmic differentiation. That is, take the natural log of both sides then compute the limit. Remember to solve for y again at the end.

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