Get Solutions and Tips for Differential Calculus Problems

College
Calculus and Analysis
Differential Calculus

Recent questions in Differential Calculus

Banguizb 2022-07-08

How to evaluate $lim_{n \to \infty} (\int_{0}^{2 π} \frac{\cos (n x)}{x^{2} + n^{2}} d x) w h e r e \forall n \in N$

rzfansubs87 2022-07-08

Infinite false limit verification via N−M method
$lim_{x \to - \infty} \frac{x^{3} + 6}{2 x^{2} - 5} = + \infty$

EnvivyEvoxys6 2022-07-08

I am having trouble finding the limit for the following function:
$lim_{x \to 0} f (x) = \frac{\tan 3 x}{\tan 2 x}$
I do not want to use L'Hospital's rule.
I know that $\frac{\tan 3 x}{\tan 2 x} = \frac{\sin 3 x \cos 2 x}{\sin 2 x \cos 3 x}$ , but that does not help me.
Can you maybe give me a hint?

Blericker74 2022-07-08

Let $f$ be any function which is defined for all numbers. Show that $g (x) = f (x) + f (- x)$ is even.

$\begin{matrix} (1) & e . g . f (x) = x^{2} ⟹ g (x) = x^{2} + (- x)^{2} = 2 x^{2} \leftarrow even \end{matrix}$

$\begin{matrix} (2) & e . g . f (x) = x^{3} ⟹ g (x) = x^{3} + (- x)^{3} = 0 \leftarrow even \end{matrix}$

$\begin{matrix} (3) & e . g . f (x) = x^{3} + x^{2} \leftarrow neither even nor odd \end{matrix}$

$\begin{matrix} (4) & ⟹ g (x) = (x^{3} + x^{2}) + (- x^{3} + x^{2}) = 2 x^{2} \leftarrow even \end{matrix}$

But how it can be proven that the claim holds?

And needless to say, can I completely assume "for all numbers" in the problem statements belong to a set of complex numbers(handling imaginary numbers is also required in this problem)?

Esmeralda Lane 2022-07-07

I got stuck trying to solve this limit.
$lim_{n \to \infty} \frac{1 + \frac{1}{2} + \frac{1}{4} + . . . . + \frac{1}{2^{n}}}{1 + \frac{1}{3} + \frac{1}{9} + . . . + \frac{1}{3^{n}}}$

ntaraxq 2022-07-07

Which rule or method can be applied against $lim_{x \to 0} \frac{\sqrt{1 + 6 x} - (1 + 3 x)}{x^{2}} ?$ ?\

fythynwyrk0 2022-07-07

Find the following limit
$lim_{N \to \infty} \frac{1}{\sqrt{N}} \sum_{n = 1}^{N} \frac{1}{\sqrt{n}} .$

Raul Walker 2022-07-07

Calculate the limit or prove it doesn't exist: $lim_{x \to 0} \frac{\sin (x)}{\frac{1}{\cos (x)} - 1}$

ziphumulegn 2022-07-07

Let f be continuous on [a,b] and differential on (a,b). Prove that if a >= 0 there are x1, x2, x3 ∈ (a,b) such that
$f^{'} (x_{1}) = (b + a) \frac{f^{'} (x_{2})}{2 x_{2}} = (b^{2} + b a + a^{2}) \frac{f^{'} (x_{3})}{3 x_{3}^{2}}$
I think this problem will use the generalized mean value theorem to solve. However, I don't know how to apply it. Can you suggest a solution? Thank you very much!

Joel French 2022-07-07

I want to prove that
$lim_{x \to - 1^{-}} \log (1 + \frac{1}{x}) - \frac{1}{1 + x} = + \infty .$

orlovskihmw 2022-07-06

The inverse function is
$f^{- 1} (x + 2) = \frac{3 x - 2}{2 x + 3}$
find
$f (\frac{1}{x - 4}) .$

antennense 2022-07-05

Compute trigonometric limit without use of de L'Hospital's rule
$lim_{x \to 0} \frac{(x + c) \sin (x^{2})}{1 - \cos (x)}, c \in R^{+}$

glitinosim3 2022-07-05

What are inverse functions?

Sylvia Byrd 2022-07-04

$lim_{x \to π / 4} \frac{\ln (\tan (x))}{x - π / 4}$
Could you help me finding the limit?

Maliyah Robles 2022-07-04

I have to calculate the following limit
$lim_{x \to + \infty} \frac{x \ln x}{1 - \sin x}$

Ayaan Barr 2022-07-04

How to prove $\underset{n \to \infty}{lim sup} | \sin (n) | = 1$ ?

Dayanara Terry 2022-07-04

Trigonometric Limit without L'hospital (0/0 kind): $lim_{x \to \frac{π}{6}} \frac{\sin (x - \frac{π}{6})}{\frac{\sqrt{3}}{2} - \cos (x)}$

Frederick Kramer 2022-07-04

The question is: $lim_{x \to 0^{+}} x^{1 / x} .$

bandikizaui 2022-07-04

Limit $lim_{x \to 0} \frac{\sin [x]}{[x]}$

Esmeralda Lane 2022-07-03

The function $(\frac{1}{x^{2}})$ is a one to one function on the interval $(0, \infty$ Find a formula for the inverse function on that domain. Sketch the graph of both functions from $0 < x < 4$ How can we choose the right sign for inverse functions?

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

Master Differential Calculus Problems with Our Experts