Calculus Examples & Word Problems Solutions

High School
Calculus and Analysis

Recent questions in Calculus and Analysis

opatovaL 2021-09-13

Suppose that you buy a lottery ticket containing k distinct numbers from among ${1, 2, . . ., n}, 1 \leq k \leq n$ . To determine the winning tickets, k balls are randomly drawn without replacement from a bin containing n balls numbered 1, 2, . . . , n. What is the probability that at least one of the numbers on your lottery ticket is among those drawn from the bin?

Jerold 2021-09-13

Find the derivatives of the functions. $e^{2 x^{2} - x + 1 / x}$

amanf 2021-09-13

Find a linear differential operator that annihilates the given function.
$f (x) = 3 x^{2} - x \sin 3 x + x^{2} e^{- x} \cos 4 x$

arenceabigns 2021-09-13

Use the Binomial Theorem to expand the binomial, ${(3 x + y)}^{3}$ and express the result in simplified form.

rocedwrp 2021-09-13

Add polynomials:
$f (x) = 2 x^{3} + 5 x^{2} - 3 x + 4$
$g (x) = x^{5} - 2 x^{2} - 1$
$f (x) + g (x) =$

Kye 2021-09-13

Find all roots of each of the of the following quartic polynomials:
a) $z^{4} + \sqrt{10} z + \frac{1}{4}$ using factorization into two quadratic polynomials

snowlovelydayM 2021-09-13

In the given equation as folows , use a computer algebra system to find the indicated Taylor polynomials for the function f. Graph the function and the Taylor polynomials :-
$f (x) = \tan π x$
$(a) n = 3, c = 0$

CoormaBak9 2021-09-13

Find all the roots (real and imaginary) of the given polynomials. Describe multiplicity when applicable. Please show all work and simplify your answers.
$f (x) = x^{4} - 8 x^{2} - 8 x + 15$

bobbie71G 2021-09-13

Determine the third and fourth Taylor polynomials of $x^{3} + 3 x - 1$ at $x = - 1$

CMIIh 2021-09-13

where 30% of all admitted patients fail to pay their bills and the debts are eventually forgiven. suppose that the clinic treats 2000 different patients over a period of 1 year, and let x be the number of forgiven debts. a. what is the mean (expected) number of debts that have to be forgiven? b. find the variance and standard deviation of x. c. what can you say about the probability that x will exceed 700?

mattgondek4 2021-09-13

Seven red and one black ball are present in Urn 1. One red ball and two black balls are in Urn 2. Five red and two black balls are in urn number three. Calculate the likelihood that a red ball will be drawn if an urn is chosen at random and then drawn.

Nann 2021-09-12

Determine the x-y coordinates of the points where the following parametric equations will have horizontal or vertical tangents $x = t^{3} - 3 t$
$y = 3 t^{2} - 9$

Marvin Mccormick 2021-09-12

$\int_{0}^{- 2} \ln | x | d x$

nitraiddQ 2021-09-12

$\int x^{3} + 3 \frac{x^{2}}{x^{2}} + 1$

Maiclubk 2021-09-12

Two balls A and B were Initially 9 m apart. Ball A moved at a speed of vA=4 m/s and ball B moved at a speed of vb=8 m/s in the directions as shown in the figure below.

Falak Kinney 2021-09-12

Polar coordinates of point P are given. Find all of its polar coordinates.
$P = (1, - \frac{π}{4})$

Cabiolab 2021-09-12

Please, find the integral $\int {(\frac{1}{\sqrt{2 x - 1}})}^{2} d x$

Marvin Mccormick 2021-09-12

Evaluate the surface integral.
$\int \int_{s} (x^{2} z + y^{2} z) d S$
S is the hemisphere $x^{2} + y^{2} + z^{2} = 9, z \geq 0$

Khaleesi Herbert 2021-09-12

Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set of parametric equations.

OlmekinjP 2021-09-12

Surface s is a part of the paraboloid $z = 4 - x^{2} - y^{2}$ that lies above the plane $z = 0$ . $(6 + 7 + 7 = 20 p t)$

a) Find the parametric equation $\vec{r} (u, v)$ of the surface with polar coordinates $x = u \cos (v), y = u \sin (v)$ and find the domain D for u and v.

b) Find ${\vec{r}}_{u}, {\vec{r}}_{v},$ and ${\vec{r}}_{u} \cdot {\vec{r}}_{v}$ .

c) Find the area of the surface

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