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If limx→4f(x)−5x−2=1, \lim_{x \to 4} \frac{f(x) - 5}{x-2}=1, x→4limx−2f(x)−5=1, find limx→4f(x). \displaystyle \lim_{x \to 4} f(x). x→4limf(x).
Given the function f(x)=6x+4x2+7x−x, f(x) = \frac{ 6x + 4}{\sqrt{x^2+7x} - x},f(x)=x2+7x−x6x+4, what is limx→−∞f(x)\displaystyle{\lim_{ x \rightarrow -\infty } f(x)} x→−∞limf(x)?
If limx→0f(x)x=6,\displaystyle \lim_{x \to 0} \frac{f(x)}{x}=6,x→0limxf(x)=6, what is the value of limx→03x2+8f(x)2x2−f(x)?\lim_{x \to 0} \frac{3x^2+8f(x)}{2x^2-f(x)}?x→0lim2x2−f(x)3x2+8f(x)?
Find the value of
limx→∞(x2+⌊x⌋−x). \lim_{x \to \infty} \left( \sqrt{x^2 + \lfloor x \rfloor} - x \right). x→∞lim(x2+⌊x⌋−x).
Assumptions and Details: ⌊⋅⌋ \lfloor \cdot \rfloor ⌊⋅⌋ is the floor function such that ⌊x⌋=n \lfloor x \rfloor = n ⌊x⌋=n if n≤x<n+1, n \leq x < n+1, n≤x<n+1, where n n n is an integer.
If limx→−1f(x+1)x+1=2, \displaystyle \lim_{x \to -1} \frac{ f(x+1) }{x+1} = 2, x→−1limx+1f(x+1)=2, find the value of limx→0x−f(x)x+f(x). \lim_{x \to 0} \frac{x - f(x)}{x+ f(x)}. x→0limx+f(x)x−f(x).
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