Secondary +
Post Secondary +
Ask Question
SECONDARY
CALCULUS AND ANALYSIS
Secondary
Calculus and Analysis
Precalculus
Calculus 1
Calculus 2
Algebra
Geometry
Statistics and Probability
Math Word Problem
Other
Post Secondary
Didn’t find what you are looking for?
Ask question
Calculus and Analysis Answers
Series
asked 2021-03-18
Find the radius of convergence, R, of the series.
\(\sum_{n=1}^\infty\frac{(2x+9)^n}{n^2}\)
Find the interval, I, of convergence of the series.
Series
asked 2021-03-18
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
\(\sum_{n=1}^\infty\frac{n^2}{(n+1)(n^2+2)}\)
Transformations of functions
asked 2021-03-18
Sketch a graph of the function. Use transformations of functions whenever possible.
\(\displaystyle{f{{\left({x}\right)}}}=-{\left({x}-{1}\right)}^{{{4}}}\)
Polynomial graphs
asked 2021-03-18
Sketch graphs of each of the following polynomial functions. Be sure to label the x- and they-intercepts of each graph.
\(\displaystyle{a}.{y}={x}{\left({2}{x}+{3}\right)}{\left({2}{x}-{5}\right)}{b}.{y}={\left({11}-{2}{x}\right)}^{{{2}}}{\left({x}-{2}\right)}\)
Matrices
asked 2021-03-18
Determine , if possible , the value of x which will male the following true:
\(\begin{bmatrix}4 & 3 \\1 & x \end{bmatrix}+2\begin{bmatrix}2 \\1 \end{bmatrix}\begin{bmatrix}3 & x \end{bmatrix}=\begin{bmatrix}16 & 11 \\7 & 6 \end{bmatrix}\)
Matrices
asked 2021-03-18
Let A and B be similar nxn matrices. Prove that if A is idempotent, then B is idempotent. (X is idempotent if
\(X^2=X\)
)
Matrices
asked 2021-03-18
Explain the term Comparable matrices?
Transformations of functions
asked 2021-03-12
Begin with the graph of y = ln x and use transformations to sketch the graph of each of the given functions.
\(\displaystyle{y}={\ln{{\left({2}-{x}\right)}}}\)
Series
asked 2021-03-12
Determine whether the series
\(\sum a_n\)
an converges or diverges: Use the Alternating Series Test.
\(\sum_{n=2}^\infty(-1)^n\frac{n}{\ln(n)}\)
Matrices
asked 2021-03-12
Find three
\(2 \times 2\)
idempotent matrices. (Recall that a square matrix A is idempotent when
\(A^2 = A\)
)
Matrices
asked 2021-03-12
Let a linear sytem of equations Ax=b where
\(A=\begin{pmatrix}4 & 2&-2 \\2 & 2&-3\\-2&-3&14 \end{pmatrix} , b=\begin{pmatrix}10 , 5 , 4 \end{pmatrix}^T\)
in case we solve this equation system by using Dolittle LU factorization method , find Z and X matrices
Series
asked 2021-03-11
Find the radius of convergence and interval of convergence of the series.
\(\sum_{n=1}^\infty\frac{x^n}{n5^n}\)
Vectors
asked 2021-03-11
These three points are on the same line: (1,2,3),(2,4,−6),(−3,−6,x). Find x. Explain your answer fully.
Series
asked 2021-03-11
Determine if the following series converges or diverges. If it is a converging geometric or telescoping series, or ca be written as one, provide what the series converges to.
\(\displaystyle{\sum_{{{k}={2}}}^{\infty}}{\frac{{{k}}}{{{k}^{{3}}-{17}}}}\)
Complex numbers
asked 2021-03-11
Determine the absolute value of each of the following complex numbers:
a. z = 5 + 12i
b. 2 - 3i.
Series
asked 2021-03-11
Taylor series and interval of convergence
a. Use the definition of a Taylor/Maclaurin series to find the first four nonzero terms of the Taylor series for the given function centered at a.
b. Write the power series using summation notation.
c. Determine the interval of convergence of the series.
\(f(x)=\log_3(x+1),a=0\)
Series
asked 2021-03-11
Determine the first four terms of the Maclaurin series for sin 2x
(a) by using the definition of Maclaurin series.
(b) by replacing x by 2x in the series for sin 2x.
(c) by multiplying 2 by the series for sin x by the series for cos x, because sin 2x = 2 sin x cos x
Limits and continuity
asked 2021-03-11
Evaluate the following limits.
\(\lim_{(x,y)\rightarrow(4,5)}\frac{\sqrt{x+y}-3}{x+y-9}\)
Matrices
asked 2021-03-11
Use cramer's rule to determine the values of
\(I_1, I_2, I_3\)
and
\(I_4\)
\(\begin{bmatrix}13.7 & -4.7 & -2.2 &0 \\ -4.7 & 15.4 & 0 &-8.2 \\-2.2 & 0 & 25.4 &-22 \\ 0 & -8.2 & -22 &31.3 \end{bmatrix}\begin{bmatrix}I_1 \\ I_2 \\ I_3 \\ I_4 \end{bmatrix}=\begin{bmatrix}6 \\ -6 \\ 5 \\-9 \end{bmatrix}\)
Matrices
asked 2021-03-11
Write each of the following linear combinations of columns as a linear system of the form in (4):
\(a) x_1\begin{bmatrix}2 \\0 \end{bmatrix}+x_2\begin{bmatrix}1 \\3 \end{bmatrix}=\begin{bmatrix}4 \\2 \end{bmatrix}\)
\(b) x_1\begin{bmatrix}1 \\2\\-1 \end{bmatrix}+x_2\begin{bmatrix}0 \\1\\2 \end{bmatrix}+x_3\begin{bmatrix}3 \\4\\5 \end{bmatrix}+x_4\begin{bmatrix}1 \\3\\4 \end{bmatrix}=\begin{bmatrix}2\\5\\8 \end{bmatrix}\)
1
2
3
4
...
45
...