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Recent questions in Differential Calculus

deal4markaz 2022-11-07

Q: State And Prove Rolles Theorem With Diagram?

pighead73283r 2022-11-07

Find the integral:
$\int \cos^{3} x d x$

MMDCCC50m 2022-11-05

Find: $f (x, y) = y^{2} + x^{2} y + x^{2} - 2 y$

Grace Mcintyre2022-11-03

Suppose f $f$ is a diﬀerentiable function that satisﬁes
3xf(x)+cos(f(x)−2)=25 $3 x f (x) + \cos (f (x) - 2) = 25$
for all x $x$ . If f(4)=2 $f (4) = 2$ , what is f′(4) $f^{'} (4)$ ?

Uriah Molina 2022-11-03

Find the integral:
$\int \cot^{3} x d x$

Ty Moore 2022-11-03

Find the integral:
$\int \cos^{2} (2 x) d x$

evitagimm9h 2022-11-03

$x^{'} = y, y^{'} = x - x^{3}$
where $(0, 0)$ is a critical point of it.
Would Lyapunov Function show a unstable critical point of system of ODE to be stable

Aleah Avery 2022-11-03

The function $f (x) = \frac{x^{2} + x}{x}$ is defined and continuous for all x except x = 0. What value of x must be assigned to f(x) for x = 0 in order that the function be continuous at x = 0?

Uriel Hartman 2022-11-03

For example, $x^{2} + y^{2} + 2 x y$ . We get $y = - x$ as a critical point.
Maximim/minimum of a critical point that is a function?

klesstilne1 2022-11-02

A plane autonomous system where there exists two ODEs, $\frac{d x}{d t} = X (x, y), \frac{d y}{d t} = Y (x, y)$ . We then usually draw trajectories on the phase plane to indicate the solutions on the plane.
If a trajectory does contain a critical point, wouldn't this trajectory just stay at that critical point rather than passing through that critical point since at that point $X = Y = 0$ and so just becomes stationary?

Ryder Ferguson 2022-10-31

How to find the oblique asymptote of root of a function?
$f (x) = \sqrt{4 x^{2} + x + 6}$

gasavasiv 2022-10-30

So I was studying topology and I came across the next theorem:
A function $f : X \to Y$ is continous iff for every $ϵ > 0$ there is $δ > 0$ such that if $d_{x} (x, y) < δ$ then $d_{y} (f (x), f (y)) < ϵ$ .
Since every distance in the uniform topology is at most 1, the theorem will always be true for any function from $R^{ω}$ to $R^{ω}$ with the uniform topology, am I wrong?

Aldo Ashley 2022-10-30

How do you prove that the function $x \cdot \frac{x - 2}{x - 2}$ is not continuous at x=2?

Nathalie Case 2022-10-30

Is it a must that all critical points are interior point for a function ?
can a boundary point be critical point of a function?

caschaillo7 2022-10-30

What type of critical point is $(0, 0)$ in the following function?
$f (x, y) \in C^{2}, T_{2} (x, y) = 3 + 2 x + 0.5 x^{2} - x y - y^{2}$

Maverick Avery 2022-10-28

Why does a nontrivial $V \to V$ have a critical point?

taumulurtulkyoy 2022-10-28

Find the integral:
$\int \csc^{3} x d x$

Chelsea Pruitt 2022-10-27

What is the definition of continuity at a point?

Paola Mayer 2022-10-27

Let us consider the identity function
$f : (R, d) \to (R, d_{u s u a l})$
$f : x \to x$
Here we are considering $d (x, y) = | (x)^{3} - (y)^{3} |$
Is the function $f$ uniformly continuous on closed and bounded interval?
I am looking for an example of function $f$ which is not uniformly continuous on a closed and bounded interval but it is continuous.

Nathalie Case 2022-10-26

Find the integral:
$\int \frac{(3 x - 2)^{2}}{x^{3}} d x$

One of the most famous and challenging aspects of learning calculus and analysis is dealing with differential calculus equations that are not too complex per se if you have an example of differential calculus sample problems that contain both answers and questions. It is recommended to use your logic and see how differential calculus problems are formed with the help of several equations where you must be solving equations with decimals, functions and their derivatives. These are used to calculate the flow of electricity, model some motion, or set the energy flow of an object in a graphical form.

Differential Calculus

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