-- sitting erect, shoulders back, chest out, head up, spine straight
-- pen held loosely and comfortably in your hand
-- forearm resting lightly on the table
-- digit characters formed neatly and clearly, with uniform size and slant
<em>3 0 9, 0 5 8, 3 0 4</em> .
Answer:
A- 8/15
Step-by-step explanation:
2/5 ÷ 3/4
= 2 × 4/5 × 3
= 8/15
Note that x² + 2x + 3 = x² + x + 3 + x. So your integrand can be written as
<span>(x² + x + 3 + x)/(x² + x + 3) = 1 + x/(x² + x + 3). </span>
<span>Next, complete the square. </span>
<span>x² + x + 3 = x² + x + 1/4 + 11/4 = (x + 1/2)² + (√(11)/2)² </span>
<span>Also, for the x in the numerator </span>
<span>x = x + 1/2 - 1/2. </span>
<span>So </span>
<span>(x² + 2x + 3)/(x² + x + 3) = 1 + (x + 1/2)/[(x + 1/2)² + (√(11)/2)²] - 1/2/[(x + 1/2)² + (√(11)/2)²]. </span>
<span>Integrate term by term to get </span>
<span>∫ (x² + 2x + 3)/(x² + x + 3) dx = x + (1/2) ln(x² + x + 3) - (1/√(11)) arctan(2(x + 1/2)/√(11)) + C </span>
<span>b) Use the fact that ln(x) = 2 ln√(x). Then put u = √(x), du = 1/[2√(x)] dx. </span>
<span>∫ ln(x)/√(x) dx = 4 ∫ ln u du = 4 u ln(u) - u + C = 4√(x) ln√(x) - √(x) + C </span>
<span>= 2 √(x) ln(x) - √(x) + C. </span>
<span>c) There are different approaches to this. One is to multiply and divide by e^x, then use u = e^x. </span>
<span>∫ 1/(e^(-x) + e^x) dx = ∫ e^x/(1 + e^(2x)) dx = ∫ du/(1 + u²) = arctan(u) + C </span>
<span>= arctan(e^x) + C.</span>
Answer:
3xy² - 14y²
Step-by-step explanation:
I hope that this is the problem
- x²y + [ - (x²y - 2xy² + y²) + (xy² - 3y² + x²y)] - (10y² - x²y)
= - x²y + [ - x²y + 2xy² - y² + xy² - 3y² + x²y] - 10y² + x²y
Now combine like terms in the [ ].
= - x²y + [ -x²y + x²y + 2xy² + xy² - y² - 3y² ] - 10y² + x²y
= - x²y + [ 0 + 3xy² - 4y²] - 10y² + x²y
= - x²y + 3xy² - 4y² -10y² + x²y Now combine like terms
= (-x²y + x²y) + 3xy² + (-4y² - 10y²)
= 0 + 3xy² - 14y²
= 3xy² - 14y² or y²(3x - 14)
Answer: 3/10
Explanation: .3 is equal to three tenths
