Write the first five terms of the sequence whose $n$th term is $a_n=(-1)^n /\left(n^2\right)$.

Find the constant $c$ such that the denominator will divide evenly into the numerator.

$$\frac{x^{5}-2x^{2}+x+c}{x+2}$$

Divide: $\left(2 x^2-5 x-3\right) \div(x-3)$

Calculate the indicated Riemann sum $S_{n}$ for the function $f(x)=25-3x^{2}$.

Partition $[-5,5]$ into five subintervals of equal length, and for each subinterval $[x_{k-1},x_{k}]$. let $c_k=(x_{k-1}+x_{k})/2$.

Rationalize the numerator or denominator of $\frac{49(x-3)}{\sqrt{x^2-9}}$ and simplify.

Find equations of the tangent plane. $x^{2}-2 y^{2}+z^{2}+y z=2, \quad(2,1,-1)$

Calculate the indicated Riemann sum $S_{n}$ for the function $f(x)=25-3 x^{2}$. Partition [0,12] into four subintervals of equal length, and for each subinterval $\left[x_{k-1}, x_{k}\right]$, let $c_{k}=\left(2 x_{k-1}+x_{k}\right) / 3$.

Calculate the indicated Riemann sum $S_{n}$ for the function $f(x)=x^{2}-5x-6$.

Partition $[0,3]$ into three subintervals of equal length, and let $c_{1}=0.7, c_{2}=1.8$, and $c_{3}=2.4$.

The function f(x) = 2x + 3 is defined on the interval [0 , 4]. approximate the area A under f from x = 0 to x = 4 as follows: Partition [0 , 4] into eight subintervals of equal length and choose u as the right endpoint of each subinterval.

Let $a=x_0<x_1<x_2 \cdots<x_n=b$ be any partition of $[a, b],$ and let $F$ be any antiderivative of $f$. Show that

$$F(b)-F(a)=\sum_{i=1}^n\left[F\left(x_i\right)-F\left(x_{i-1}\right)\right] .$$

Divide. $\left(36 x^{2}-81\right) \div(6 x+9)$

Rationalize the numerator of the expression. Then simplify your answer. $\frac{\sqrt{12}}{2}$

Calculate the indicated Riemann sum $S_{n}$ for the function $f(x)=x^{2}-5 x-6$. Partition [1,7] into six subintervals of equal length, and let $c_{1}=1, c_{2}=3, c_{3}=3, c_{4}=5, c_{5}=5$, and $c_{6}=7$.

Rationalize the numerator of the expression. Then simplify your answer. $\frac{\sqrt{7}-3}{4}$