Get Your Calculus 1 Questions Answered Here!

Evaluate $lim_{(x, y) \to (0, 0)} \frac{\sin (x^{2} + y^{2})}{c d}$

Ernesto Wagner 2022-11-23

How to solve an equation like $2^{x} + x = 2$ ?

armlanna1sK 2022-11-23

If $f (n) = (\sqrt{n})^{\sqrt{n}}$ and $g (n) = (\lg n)^{n}$ , is $f (n) = O (g (n))$ or $g (n) = O (f (n))$ ?

BertonCO5 2022-11-23

If $x^{x} y^{y} z^{z} = c$ , show that at $x = y = z, z_{x y} = - (x \log x)^{- 1}$
I applied logarithmic functions on both sides, ultimately it led to a satisfying result where most things canceled out, but unfortunately, it wasn't the right answer.

Talia Frederick 2022-11-23

If $f (x) = e^{- x} + 2 e^{- 2 x} + 3 e^{- 3 x} + \dots$ then find $\int_{\ln 2}^{\ln 3} f (x) d x$

Kyler Oconnor 2022-11-22

Given a $C^{2}$ L-smooth function the Lipschitz condition is:
$| | \nabla f (x) - \nabla f (y) | | \leq L | | x - y | |$
Are these conditions only true for convex $C^{2}$ function? What will change If $f$ is $C^{2}$ and concave?

Jamie Medina 2022-11-22

Need a hint to evaluate the indefinite integral $\int \frac{e^{x} (2 - x^{2})}{(1 - x) \sqrt{1 - x^{2}}} d x$

Emma Hobbs 2022-11-22

Let $L (X) = \exp (\sqrt{\log X \log \log X})$
Prove that if c>0, $Y = L (X)^{c}$ , and $u = \log X / \log Y$ , then
$u^{u} = L (X)^{(1 / 2 c) (1 + o (1))}$
I've tried to write $u^{u} = (\log X / \log Y)^{\log X / \log Y}$
But that doesn't seem to get me anywhere.

Ty Moore 2022-11-22

Does the property of non-increasing slope be generalized to a concave function for multiple variables?

unabuenanuevasld 2022-11-21

Let $f : Ω \subseteq R^{n} \to R_{\geq 0}$ be a continuous differentiable function over $Ω$ . Suppose that the function $f$ is concave, and fix two points $x = (x_{1}, \dots, x_{n}), y = (y_{1}, \dots, y_{n}) \in Ω$ , $x = (x_{1}, \dots, x_{n}), y = (y_{1}, \dots, y_{n}) \in Ω$ .
If $x_{i} \leq y_{i}$ for all $i = 1, \dots, n$ and $Ω = R^{n}$ , does it hold $∥ \nabla_{x} f ∥\geq∥ \nabla_{y} f ∥$ ?

Abdiel Mays 2022-11-21

If the function $f (x) = \log_{2 x} x^{2}$ is given, what is $f^{'} (4)$ ?
I tried to use the formula for derivative of logarithm but here the base is 2x, so it made me confused.
Note that the answer is $1 / (18 \ln 2)$

Elliana Molina 2022-11-20

Evaluate
$\int_{0}^{1} (x^{5} + x^{4} + x^{2}) \sqrt{4 x^{3} + 5 x^{2} + 10} d x$

Adrian Brown 2022-11-20

Let $f \in C^{2}$ (i.e, $f$ is differentiable twice and $f^{'}, f^{″}$ are continuous. Show that $f$ can be written as $f (x) = g (x) + h (x)$ where $g (x)$ is convex for any $x$ and $h (x)$ is concave for any $x$ .

Clara Dennis 2022-11-20

The function is
$\int \frac{1}{1 + \sqrt{2 x}} d x$
Using $u = 1 + \sqrt{2 x}$ , $d u = \frac{1}{\sqrt{2 x}} d x$ . Which gives us
$\sqrt{2 x} \int \frac{1}{u} d u$
The final answer of this would give $\sqrt{2 x} \ln | 1 + \sqrt{2 x} |$ , but when I checked my answer the correct answer is $\sqrt{2 x} - \ln | 1 + \sqrt{2 x} |$

Demarion Ortega 2022-11-20

Prove $\int_{0}^{\infty} \frac{\sin^{4} x}{x^{4}} d x = \frac{π}{3}$

inurbandojoa 2022-11-20

Let $f (x)$ be an increasing, strictly concave function with $f (0) = 0$ . Show that given $x < y$ , $f (y + ε) - f (x + ε) < f (y) - f (x)$ , where $ε$ is a small, positive number.

django0a6 2022-11-20

f(0)=10, f(12)=8, f(24)=7 f(36)=6,5, f(48)=6. I know how to construct an exponential function if I have two points, but I don't know how to create this function, or that such exponential functian even exists.

Melissa Walker 2022-11-19

Integral inequality: $\frac{1}{30} < \int_{2}^{\infty} \frac{\sqrt{s^{3} - s^{2} + 3}}{s^{5} + s^{2} + 1} d s < \frac{\sqrt{2}}{20}$

Aleah Avery 2022-11-19

How can I show that the exponential function, $a^{x}$ , $a \in R^{+} - {1}$ is injective? I want to not use the inverse log function as originally I was trying to come up with algebraic justification of why the log function is well-defined and it looks like I can show that assuming the exponential function $a^{x}$ is injective. It looks like showing the function is injective is equivalent to showing that $a^{x}$ =1 implies x=0. Now I am trying to figure out some kind of contradiction if $x \neq 0$ .

Rigoberto Drake 2022-11-19

Solve each of the following equations for x.
a) $\ln (5 x) = 0 x = ?$
b) $\log_{5} (2 x) + \log_{5} (4 x) = 2 x = ?$

The majority of Calculus 1 questions and answers that you will find below should be sufficient for understanding the basic rules that are necessary for problem-solving purposes. Take a look at the original answers, seek math assignment help, and compare them to what you have for your assignment.

If you need any other kind of help for your Calculus 1 tasks, combine several solutions or look at the problem that seems similar to your original assignment. If Math is not your subject per se, start with the most basic problems and proceed with the complex ones.

Calculus 1

Master Calculus 1 Practice Problems with Expert Help