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Limits and continuity

Evaluate the following limits. $$\lim_{(x,y)\rightarrow(4,5)}\frac{\sqrt{x+y}-3}{x+y-9}$$

Limits and continuity

Find each of the following limits. If the limit is not finite, indicate or for one- or two-sided limits, as appropriate. $$\lim_{x\rightarrow\infty}\frac{4x^3-2x-1}{x^2-1}$$

Limits and continuity

Evaluate the following limits. $$\lim_{(x,y)\rightarrow(2,2)}\frac{y^2-4}{xy-2x}$$

Limits and continuity

Integrals

Evaluate the following integrals. $$\int_0^1\frac{16^x}{4^{2x}}dx$$

Limits and continuity

Use the method of your choice to evaluate the following limits. $$\lim_{(x,y)\rightarrow(4,0)}x^2y\ln xy$$

Limits and continuity

Find the limits: $$\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}$$

Limits and continuity

Use the method of your choice to evaluate the following limits. $$\lim_{(x,y)\rightarrow(2,0)}\frac{1-\cos y}{xy^2}$$

Analyzing functions

Polynomial function's f(x) coefficients are real numbers. Find the remaining zeros of f. Degree 6, zeros: i, 3 - 2i, -2 + i

Limits and continuity

Find the following limit: $$\lim_{x\rightarrow0}\frac{xe^x}{e^{3x}-1}$$

Limits and continuity

Evaluate the following limit. $$\lim_{h\rightarrow0}\frac{100}{(10h-1)^{11}+2}$$

Limits and continuity

Evaluate the following limits. $$\lim_{(x,y)\rightarrow(1,-2)}\frac{y^2+2xy}{y+2x}$$

Limits and continuity

Find the following limits or state that they do not exist. $$\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}$$

Limits and continuity

Integrals

Evaluate the following iterated integrals. $$\int_0^3\int_{-2}^1 (2x+3y)dxdy$$

Limits and continuity

Find the function The following limits represent the slope of a curve y=f(x) at the point {a,f(a)} Determine a possible function f and number a, then calculate the limit $$\lim_{x\rightarrow2}\frac{5\cdot x^2-20}{x-2}$$

Limits and continuity

Find the limit $$\lim_{x\rightarrow-\infty}\frac{x^2-4x+8}{3x^3}$$

Limits and continuity

Integrals