promath Answer: The integration of Sec2x is equal to (1/2) ln|Sec2x+tan2x|+C. So the formula for the integral of Sec 2x is given by $\displaystyle \int \sec 2x~dx=\dfrac{1}{2}\ln|\sec 2x +\tan 2x|$ $+C$ where C denotes an integral constant. Note: To find the integral of sec2x, we will use the integral of secx which is as follows: $\displaystyle … Read more
Answer: 4/8 as a fraction simplified in its reduced form is equal to 1/2. Here, we learn how to simplify 4/8 into its simplest form. What is 4/8 in Simplest Form? Answer: 4/8 in simplest form is equal to 1/2. Solution: Method 1: Division Method To simplify the fraction 4/8, let us use the division … Read more
Answer: 4/6 as a fraction simplified in its reduced form is equal to 2/3. Here, we learn how to simplify 4/6 into its simplest form. What is 4/6 in Simplest Form? Answer: 4/6 in simplest form is equal to 2/3. Solution: Method 1: Division Method To simplify the fraction 4/6, let us use the division … Read more
Answer: 6/8 as a fraction simplified in its reduced form is equal to 3/4. Here, we learn how to simplify 6/8 into its simplest form. What is 6/8 in Simplest Form? Answer: 6/8 in simplest form is equal to 3/4. Solution: Method 1: Division Method To simplify the fraction 6/8, let us use the division … Read more
Fractions with the same denominator are called like fractions. For example, 1/5 and 4/5. On the other hand, fractions with different denominators are called unlike fractions. For example, 1/5 and 4/7. Here, let us learn like fractions and unlike fractions with definition, examples and their differences. Definition of Like Fractions Two fractions are said to … Read more
Answer: The limit of x^x as x approaches 0+ is equal to 1. That is, limx→0+ xx = 1. Limit of xx when x tends to 0+ Question: Find the limit of xx when x tends to 0+? Solution We need to find limx→0+ xx. Step 1: Note that x = eln x ⇒ $x^x … Read more
Answer: The derivative of x^2 sin(1/x) at x=0 is equal to 0 if the function is defined to be 0 at x=0. Question Find the derivative of the function f(x) = $\begin{cases} x^2 \sin(\frac{1}{x}) & \text{if } x \neq 0 \\ 0 & \text{if } x=0 \end{cases}$ at x=0. That is, find f'(0). Solution From … Read more
The integral of e^(-x^2) from negative infinity to infinity is equal to √π, that is, $\int_{-\infty}^\infty$exp(-x^2) dx = √π. Here we will learn how to integrate e-x^2 (e to the power minus x2) from -∞ to ∞. Integral of exp(-x^2) from Minus Infinity to Infinity Answer: The integral of $e^{-x^2}$ from -∞ to ∞ is … Read more
The integral of e^(-x^2) from 0 to infinity is equal to √π/2, that is, ∫exp(-x^2) dx = √π/2. Here we will learn how to integrate e-x^2 (e to the power -x2) from 0 to ∞. Integration of exp(-x^2) from 0 to infinity Answer: The integral of $e^{-x^2}$ from 0 to infinity is equal to √π/2. … Read more
The Laplace transform of sint/t is equal to tan-1(1/s), that is, L{sint/t} = tan-1(1/s). The formulas for the Laplace of sint/t and the Laplace of sin(at)/t are given as follows: $\boxed{\mathcal{L}\left\{\dfrac{\sin t}{t} \right\}=\tan^{-1}\left(\dfrac{1}{s} \right)}$ and $\boxed{\mathcal{L}\left\{\dfrac{\sin at}{t} \right\}=\tan^{-1}\left(\dfrac{a}{s} \right)}$ Lets learn how to find Laplace of sin(t)/t. Laplace of sint/t Question: What is the Laplace … Read more