Suppose that lim x → a f ( x ) = ∞ and lim x → a g ( x ) = c , where c is a real number. Prove each statement. (a) lim x → a [ f ( x ) + g ( x ) ] = ∞ (b) lim x → a [ f ( x ) g ( x ) ] = ∞ if c > 0 (c) lim x → a [ f ( x ) g ( x ) ] = − ∞ if c < 0
Suppose that lim x → a f ( x ) = ∞ and lim x → a g ( x ) = c , where c is a real number. Prove each statement. (a) lim x → a [ f ( x ) + g ( x ) ] = ∞ (b) lim x → a [ f ( x ) g ( x ) ] = ∞ if c > 0 (c) lim x → a [ f ( x ) g ( x ) ] = − ∞ if c < 0
Solution Summary: The author explains the value of the function undersetxto amathrmlimleft.
Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6 f(x) = L, and prove that the limit is correct by completing a δ − ε proof for the limit of the function.
For any real number r, it can be shown that lim x--> ∞ x^r/e^x = 0. Using this fact what is lim x--> ∞ e^x + x^2023/e^2x + x^2
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