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Find the value of
limx→∞2x+sinxx+cosx. \lim_{x \to \infty} \frac{2x + \sin x}{x + \cos x}. x→∞limx+cosx2x+sinx.
Suppose a polynomial function f(x)f(x) f(x) satisfies limx→1f(x)+2x−1=3. \lim_{x \to 1} \frac{f(x)+2}{x-1} = 3.x→1limx−1f(x)+2=3. Find the value of limx→−1[f(−x)]2−4x2−1. \lim_{x \to -1} \frac{[f(-x)]^2 - 4}{x^2 -1}. x→−1limx2−1[f(−x)]2−4.
Evaluate limx→−∞36x2+2613−x12\displaystyle \lim_{x \to -\infty} \frac{\sqrt{36 x^2 + 26}}{13 - \frac{x}{12}}x→−∞lim13−12x36x2+26.
Consider the function f(x)=ax3+bx2+10x−20x2−1.f(x) = \displaystyle \frac{ax^3+bx^2+10x-20}{x^2-1}.f(x)=x2−1ax3+bx2+10x−20. If limx→∞f(x)=10,\displaystyle \lim_{x \to \infty}f(x)=10,x→∞limf(x)=10, what is the value of limx→1f(x)?\displaystyle \lim_{x \to 1}f(x)?x→1limf(x)?
For the function f(x)=∣x(x+2)∣x(x+1), f(x) = \frac{ |x(x+2)| }{ x(x+1) }, f(x)=x(x+1)∣x(x+2)∣, find the value of limx→−2+f(x)+limx→0+f(x). \lim_{x \to -2^+} f(x) + \lim_{x \to 0^+} f(x). x→−2+limf(x)+x→0+limf(x).
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