Calculus Examples & Word Problems Solutions

High School
Calculus and Analysis

Recent questions in Calculus and Analysis

vestirme4 2021-10-13

Find the limit and discuss the continuity of the function.
$lim_{(x, y) \to (- 1, 1)} (x + 4 y^{2} + 5)$

aortiH 2021-10-13

Find an equation for the plane consisting of all points that are equidistant from the points (1,0,-2) and (3,4,0) .

Jaden Easton 2021-10-13

Tell which of the following subsets are subspaces of the vector space of nxn matrices, $M_{n x n}$
a) The set of nxn matrices with a zero determinant.
b) The invertible matrices.
c) The diagonal matrices.
d) Upper triangular matrices.
e) The nxn matrices, all of $M_{n x n}$ .

a2linetagadaW 2021-10-13

Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist)
$lim_{h \to 0} \frac{{(1 + h)}^{2} - 1^{2}}{h}$

pedzenekO 2021-10-13

Use limit theorems as needed to evaluate each of the following limits; if a limit is real number, find it; if a limit is infinite, find which one; and if a limit does not exist, then write DNE.
$lim_{x \to 2} \frac{(x + 1) (x^{2} - 4)}{x^{2} - 3 x + 2}$

Haven 2021-10-13

Evaluate the following limits, where c and k are constants.
$lim_{h \to 0} \frac{{(5 + h)}^{2} - 25}{h}$

Cabiolab 2021-10-13

Find the limit and discuss the continuity of the function.
$lim_{(x, y) \to (- 1, 2)} \frac{x + y}{x - y}$

permaneceerc 2021-10-13

Find the limit, is the function continuous at the point being approached
$lim_{x \to \frac{π}{6}} \sqrt{\csc^{2} x + 5 \sqrt{3} \tan x}$

Line 2021-10-12

Evaluate the limit using continuity.
$lim_{(x, y) \to (1, 2)} (x^{2} + y)$

Nann 2021-10-12

Find the gradient vector field of f.
$f (x, y) = \tan (3 x - 4 y)$

vestirme4 2021-10-12

Analyzing critical points.
Use the Second Derivative Test to classify the critical points of $f (x, y) = x^{2} + 2 y^{2} - 4 x + 4 y + 6$ .

Dottie Parra 2021-10-12

Use a double integral to find the volume of the indicated solid. $z = 6 - 2 y, 0 \leq x \leq 4, 0 \leq y \leq 2$

avissidep 2021-10-12

Use the LHospitals

vazelinahS 2021-10-12

Find the limits
$lim_{x \to \infty} \sqrt{\frac{8 x^{2} - 3}{2 x^{2} + x}}$

Anonym 2021-10-12

To determine
(1) If f and g are both even functions, whether $f + g$ is even?
(2) If f and g are both odd functions, whether $f + g$ is odd?
(3) If f is even and g is odd function, what will $f + g$ ?

rocedwrp 2021-10-12

Evaluate the following limits algebraically. If neccessary, select the most informative answer from infinity, negative infinity, and DNE (Does Not Exist)
$lim_{x \to 0} \frac{3}{x^{2}}$

ankarskogC 2021-10-12

Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.
$lim_{x \to 0} \frac{x}{\sqrt{c x + 1} - 1}, c \neq 0$

postillan4 2021-10-12

What do the limits $lim_{h \to 0} \frac{\sin h}{h}$ and $lim_{h \to 0} \frac{\cos h - 1}{h}$ have to do with the derivatives of the sine and cosine functions? What are the derivatives of these functions?

Nannie Mack 2021-10-12

What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral formulas? What similarities do you see here to the six basic trigonometric functions?

Tyra 2021-10-12

Inverse Trigonometric Functions Are the derivatives of the inverse trigonometric functions algebraic or transcendental functions? Explain.

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