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In the arithmetic sequence $\{a_n\}$, it is known that $a_1 + a_2 + a_3 = 6$

Given the vectors $\mathbf{a} = (2,-1)$ and $\mathbf{b} = (4,m)$

Sum of the series $\frac{1}{1\cdot 2\cdot 3\cdot 4}+\frac{4}{3\cdot 4\cdot 5\cdot 6}+\cdots$

Evaluate the limit $\lim_{n\to\infty}\sum_{i=1}^{n} f(c_i)\,\Delta x_i$ for $f(x)=\sqrt{x}$

Determine the vertical asymptotes of $f(x)=\frac{2x^2-3x+5}{x^2-5x+6}$

GIVEN: $AC > AB$, $DE \cong CE$. PROVE: $AB$ is not parallel to $DE$.

3 Modular arithmetic 3.1 Equivalence relations and partitions

Choose the law and the formula that would be used to solve the triangle.

$SA = 2\pi(6^2) + 2\pi(6)(2)$

For the following exercises, find the domain of each function using interval notation.

Evaluate $f(-3), f(-2), f(-1)$ and $f(0)$

In $\triangle OAB$, P and Q are the midpoints of sides $OA$ and $OB$ respectively. $AQ$ intersects $BP$ at $M$

$$\frac{d}{dt}\int_a^b f(x,t)\,dx=\int_a^b \partial_t f(x,t)\,dx$$

The figure above shows the region A, which is bounded by the x- and y-axes, the graph of $f(x)=\frac{\sin x}{x}$

If $F(x)=\int_0^x f(t)\,dt$, and $F(a)=-2$ and $F(b)=-2$

Let $f(x)=\int_{-2}^{x^2-3x} e^{t^2}\,dt$

Average rate of change of $f(x)=\int_{1}^{x}\sqrt{t^{3}+2}\,dt$ on $[0,3]$

Evaluate $\int_0^{\pi/2} [9\sin(3x)]\,dx$

If $\int_3^5 p(x)\,dx=3$ and $\int_8^5 p(x)\,dx=1$, then what is the value of $\int_3^8 (p(x)+1)\,dx$?

Evaluate $\int_0^4 (6x^2-16x+2)\,dx$