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Calculus Worksheets - Tải xuống bản PDF miễn phí

Giới hạn

Basic

Substitution

1.\:\:\lim _{x\to 0}(\frac{1}{2})

2.\:\:\lim _{x\to 1}(2x^2-3x+5)

3.\:\:\lim _{x\to 2}(x(x-3))

4.\:\:\lim _{x\to 3}(\frac{3-x}{x^2+2x})

5.\:\:\lim _{x\to -1}(\frac{x+1}{x-1})^2

6.\:\:\lim _{x\to 5}(\frac{x^2-6x+8}{x-4})

7.\:\:\lim _{x\to -3}(\frac{(x-6)}{(5x^2-6x+8)})

8.\:\:\lim _{x\to 0}(\sqrt{x})

9.\:\:\lim _{x\to 3}(\frac{5x^{2}-8x-13}{x^{2}-5})

10.\:\:\lim _{x\to -7}(2x+5)

Giới hạn

Moderate

Limits at Infinity

1.\:\:\lim _{x\to \infty}(\frac{1}{x})

2.\:\:\lim _{x\to -\infty}(\frac{1}{x})

3.\:\:\lim _{x\to \infty}(x^2)

4.\:\:\lim _{x\to \infty}(x^3-x)

5.\:\:\lim _{x\to \infty}(5x^2+4x)

6.\:\:\lim _{x\to \infty}(2x^4-x^2-8x)

7.\:\:\lim _{x\to -\infty}(x^4+x^5)

8.\:\:\lim _{x\to \infty}(\frac{1}{x^{2}})

9.\:\:\lim _{x\to \infty}(e^x)

10.\:\:\lim _{x\to -\infty}(e^x)

Series

Convergence Tests

Geometric Series Test

1.\:\:convergence\:\sum_{n=0}^{\infty}\frac{1}{2^{n}}

2.\:\:convergence\:\sum_{n=0}^{\infty}\frac{1}{e^{n}}

3.\:\:convergence\:\sum_{n=0}^{\infty} (-1)^{n}

4.\:\:convergence\:\sum_{n=0}^{\infty}2^{n}

5.\:\:convergence\:\sum_{n=0}^{\infty} (\frac{e}{10})^{n}

6.\:\:convergence\:\sum_{n=0}^{\infty} (\frac{2}{3})^{n}

7.\:\:convergence\:\sum_{i=0}^{\infty} (\frac{1}{5})^{i}

8.\:\:convergence\:\sum_{n=0}^{\infty} (\frac{e}{\pi})^{n}

9.\:\:convergence\:\sum_{n=0}^{\infty} \frac{1}{3^{n}}

10.\:\:convergence\:\sum_{n=0}^{\infty} 0.5^{n}

Series

Absolute Convergence

Absolute Convergence

1.\:\:\sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}}

2.\:\:\sum_{n=1}^{\infty}\frac{(-1)^{n}n^{100}}{4^{n}}

3.\:\:\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{\ln(n^{n})}

4.\:\:\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{\ln^n(n)}

5.\:\:\sum_{n=1}^{\infty}(-1)^{n}\frac{n}{\sqrt{n^{3}+2}}

6.\:\:\sum_{n=1}^{\infty}(-1)^{n+1}\frac{3^{n}n^{6}}{n!}

7.\:\:\sum_{n=1}^{\infty}\frac{(-1)^{n}}{n^{\frac{2}{3}}}

8.\:\:\sum_{n=1}^{\infty}\frac{(-3)^{n-1}}{4^{n}}

9.\:\:\sum_{n=1}^{\infty}(-1)^{n}(\frac{\ln(n)}{\ln(n^{2})})^{n}

10.\:\:\sum_{n=0}^{\infty}\frac{\cos(nπ)}{5^{n}}

Tích phân

Basic

Constant Rule

1.\:\:\int \frac{1}{3}dx

2.\:\:\int 0.5dx

3.\:\:\int \frac{20}{16}dx

4.\:\:\int \frac{1}{2}dx

5.\:\:\int \frac{3}{4}dx

6.\:\:\int \frac{1}{4}dx

7.\:\:\int 2.4dx

8.\:\:\int -\frac{1}{7}dx

9.\:\:\int -\frac{2}{3}dx

10.\:\:\int 1.8dx

Tích phân

Moderate

Substitution

1.\:\:\int \sin(2x+5)dx

2.\:\:\int \sin(-3x)dx

3.\:\:\int \sin(1-x)dx

4.\:\:\int \cos(2x+1)dx

5.\:\:\int \sin(x+1)dx

6.\:\:\int \cos(3x+2)dx

7.\:\:\int \cos(2x+5)dx

8.\:\:\int \sin(x-7)dx

9.\:\:\int \cos(-2x)dx

10.\:\:\int \sin(3x+4)dx

Multiple Integrals

Double

Double

1.\:\:\int_{-2}^{1}\int_{0}^{\sqrt{4-y^{2}}}xy^{2}dxdy

2.\:\:\int_{0}^{9}\int_{-\frac{\pi}{2}}^{\frac{\pi }{2}}e^{-r^{2}}rdrd\theta

3.\:\:\int_{0}^{2}\int_{\frac{y}{2}}^{1}x^{2}ydxdy

4.\:\:\int_{0}^{1}\int_{0}^{1}xydxdy

5.\:\:\int_{0}^{3}\int_{0}^{2}3x^{2}y^{3}dxdy

6.\:\:\int_{0}^{4}\int_{1}^{5}(y^{2}+3x^{2})dxdy

7.\:\:\int_{1}^{2}\int_{0}^{1}x^{2}ydxdy

8.\:\:\int_{0}^{4}\int_{0}^{4}e^{(4x+5y)}dxdy

9.\:\:\int_{0}^{2\pi}\int_{0}^{\sqrt{5}}\sqrt{4+r^{2}}rdrd\theta

10.\:\:\int_{0}^{\frac{\pi}{2}}\int_{0}^{1+\cos(\theta )}\sin(\theta )rrdrd\theta

Đạo hàm

Basic

Constant Rule

1.\:\:\frac{d}{dx}(1)

2.\:\:\frac{d}{dx}(\frac{2}{3})

3.\:\:\frac{d}{dx}(\sin(\frac{\pi}{2}))

4.\:\:\frac{d}{dx}(3a)

5.\:\:\frac{d}{dx}(n^2)^{\frac{1}{3}}

6.\:\:\frac{d}{dx}(-4)

7.\:\:\frac{d}{dx}(\sqrt{3})

8.\:\:\frac{d}{dx}(\frac{1}{2})

9.\:\:\frac{d}{dx}(6)

10.\:\:\frac{d}{dx}(a)

Đạo hàm

Moderate

Trig Functions

1.\:\:\frac{d}{dx}(x\sin(x)+\cos(x))

2.\:\:\frac{d}{dx}(\frac{\tan(x)}{\pi x})

3.\:\:\frac{d}{dx}(\frac{\sin(x)+1}{\cos(x)-1})

4.\:\:\frac{d}{dx}(\pi\cot(x))

5.\:\:\frac{d}{dx}(\tan(x)\sin(x))

6.\:\:\frac{d}{dx}(4\sin(x))

7.\:\:\frac{d}{dx}(\tan(x)-x)

8.\:\:\frac{d}{dx}(\pi\csc(x))

9.\:\:\frac{d}{dx}(\frac{\sin(x)}{2x})

10.\:\:\frac{d}{dx}(\cos(x)\sin(x))