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Answers by Christopher G.

What's f(x)? (answer)

This requires integration by parts, which allows us to solve the integral of the product of two functions.   ∫ x2cosx dx   This integral has two functions being multiplied together, x2 and cosx. One of these we will assign to be itself, or u, and the other will be the derivative...

What's h'(x)? (answer)

h(x) = f2(x) - g2(x) h'(x) = [f2(x) - g2(x)]' = [f2(x)]' - [g2(x)]'   We need to use the chain rule to find [f2(x)]' and [g2(x)]', that is, we need to take the derivative of (something)2, which is 2(something), and then multiply that by the derivative of that something.   [f2(x)]'...

Find the slope? (answer)

Yes, the correct answer is 4. And you're right, you don't need the point or y-intercept since all you need is the derivative at that point (the slope) to find the normal slope.

Which number is a multiple of 6? (A) 2 (B) 3 (C) 42 (D) 1 (answer)

A multiple of a number is any product of that number with another number. For 6, the first few multiples are 6 × 1, 6 × 2, 6 × 3, 6 × 4, 6 × 5 ... which are 6, 12, 18, 24, 30, and so on. 42 is a multiple of 6, since 6 × 7 = 42. So the answer is C. The other choices (2,...

How do you prove log(a^x) = 1/log(x^a) (answer)

This is not a true statement. Use the same values for x and a to see why.   I think what you might have meant is logax = 1/logxa, (where the a on the left-hand side and the x on the right-hand side are the bases of the logarithms, not the bases of an exponent) which is true and can...

f(x)=x^2/3 (2-x) = x^2/3 (2-x) (answer)

f(x) = x2/3(2 - x)   I would first distribute to make it easier to derive (otherwise we would have to use the product rule and that can get messy).   f(x) = 2x2/3 - x5/3     (remember x is really x1 or x3/3 in this case, so x2/3 times x3/3 is x5/3)   Now...

how to graph a rational function (answer)

When graphing a rational function, find the x-intercepts, y-intercepts, vertical asymptotes, and horizontal asymptotes. x-intercepts: x-values when y = 0 (hint: y = 0 only when the numerator = 0)      0 = x + 3     ->     x = -3, or (-3, 0) y-intercepts: y-values...

describe the nature of the roots of the equation 7x^(2)=4x+1 (answer)

Put the equation in standard form by bringing the 4x + 1 to the left side. 7x2 - 4x - 1 = 0 We use the discriminant to determine the nature of the roots of a quadratic equation. The discriminant is the expression underneath the radical in the quadratic formula: b2 - 4ac.  b2...

which term is linear term in the equation y=2x^(2)-3x+5 (answer)

A linear term is a term with a degree of 1, or simply x. In this example, 2x2 is a quadratic term because the x has a degree of 2, and the 5 is just a constant. -3x is the linear term because its degree is 1 (x1 or simply x). Think of it this way too: a linear equation is in the form y =...

simplifyv(x^(4))+v3:(x^(6))+v4:(x^(8)) (answer)

It's easiest to rewrite this using exponents. Remember that a radical becomes a fractional exponent. √(x4) + 3√(x6) + 4√(x8) = (x4)1/2 + (x6)1/3 + (x8)1/4 Now simply multiply the exponents: x4/2 + x6/3 + x8/4 = x2 + x2 + x2 = 3x2...

express the following using exponentsv4:(32x^(8)y^(3)) (answer)

Since the answers are all in fractional exponents, I'm going to rewrite the expression that way: 4√(32x8y3) = (32x8y3)1/4 = (32)1/4(x8)1/4(y3)1/4 32 = 25, so (32)1/4 = (25)1/4 = 25/4 For the variables, simply multiply the exponents: (x8)1/4 = x(8 × (1/4)) = x2 (y3)1/4 =...

identify the vertex of the parabola defined by y=2x^(2)+8x+9 (answer)

To find the x-coordinate of the vertex, you use the formula -b/2a. (Remember that the standard form of a quadratic is y = ax2 + bx + c.) So in this case b = 8 and a = 2. -b/2a = -8/(2·2) = -8/4 = -2 Now to find the y-coordinate, simply plug the x-value into the quadratic equation...

simplify:5+2v(6)-3v(6)+9 (answer)

It's helpful to think of radicals like variables when adding or subtracting. So just as 2x and 3x are like terms with the same variable (and therefore can be combined), 2√(6) and -3√(6) are like terms with the same radical and can be added together. 5 + 2√(6) - 3√(6) + 9 14 - 1√(6)...

simplify (-3v(24))(5v(20)) (answer)

To multiply radical expressions, remember to multiply the coefficients together and the radicals together. (-3√(24))(5√(20)) = (-3)(5) × √((24)(20)) = -15√(480) You might be inclined to pick choice B now, but remember that you can simplify the radical. 480 = 16 × 30    ...

simplify: (7)/(4-v(3)) (answer)

  To simplify a radical in the denominator, you need to rationalize by multiplying both the numerator and denominator by its conjugate. The conjugate is the same expression but with the opposite sign. In this case, the conjugate of 4 - √3 is 4 + √3.    7...