Explanation

$$lim_{x to a} (2x + 4)$$

Assuming the question meant:

lim​ x→3 ​(2x+4)

Then:

$$lim_{x to 3} (2x + 4) = 2(3) + 4 = 6 + 4 = 10$$x→3 (2x+4)=2(3)+4=6+4=10

Explanation

The given differential form can be rewritten as:

xdy - ydx/x^2 = d(y/x) - (y/x^2)dx

Using the quotient rule for derivatives, we can simplify this to:

d(y/x) - (y/x^2)dx = d(ln(y/x))

Explanation

Let's simplify the expression:

∜256a⁴b⁴ = ∜(4⁴ × a⁴ × b⁴)

= ∜(4a × 4a × 4a × 4a × b × b × b × b)

= 4ab

Explanation

Explanation

$$= frac{10 - 1}{10^{10}} = frac{9}{10^{10}} = 9 times 10^{-11}$$

Explanation

Let u = 5x, du/dx = 5, du = 5dx, dx = du/5

∫sin5xdx = (1/5)∫sinu du

= (1/5)(-cosu) + c

= -1/5cos5x + c

Explanation

¬p (read as "not p") represents the negation of statement p.

In this case, p is the statement "x + y = 3".

The negation of this statement would be "x + y ≠ 3", which means any situation where x + y is not equal to 3.

Explanation

To find the value of (4 + a)(4 - b), substitute a = 4 and b = -4:

(4 + 4)(4 - (-4))

= (8)(8)

= 64

Explanation

The formula for the volume of a solid of revolution around the x-axis is π ∫[a, b] (f(x))^2 dx, where f(x) is the function being rotated, and a and b are the limits of integration.

Explanation

If $f(x) = 5$, then what is$f'(x)$ at $x = 1$?

This is a constant function, meaning:

$$f(x) = 5 quad text{for all } x$$

The derivative of a constant is always:

$$f'(x) = 0$$