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I was given this equation (1)/(x) (dy)/(dx) = y ex2 + 2 squareroot(y) ex2 and was told to solve it.. I know that i have to collect all the y terms on one side and all the x terms on the other, and then im supposed to take the integral of both sides and simplify as much as possible. But i...

I usually don't have a problem finding the derivative of functions, but this particular expression is driving me nuts. I was given this expression sin2(x/3) and I was told to find the derivative. From what I know, I know that sin2(x/3) is the same as (sin (x/3))2 So I first used the chain...

I was given this problem y = log16 ex - log4 sixth square root(x) I know the derivative of log4 sixth square root(x) , it's just (1)/(6x log 4). But i'm a little confused about the derivative of log16 ex .. if i apply the law of logarithms, then i get x log16 e... but i don't know what to do...

f(x) = x3 tan x g(x) = sin(e3x + 2) h(x) = (x2 + 1)/(cos x) For the first one, i used the product rule for derivatives.. (3x2)(tan x) + (sec2x)(x3) 3x2 tan x + x3 sec2x (this is my answer) For the second one, i used the chain rule for derivatives.. f'(g(x)) * g'(x) f(u) = sin u...

Find the limit as x goes to positive infinity of this function f(x) = (sin 10x)/(18x) I know the answer is just 0, but i want to know the actual steps require to get the answer. Can anyone show me the steps?

I was given this problem.. y = (cos x)/(5x) and i was asked to determine at which points is this function continuous? I know I can just graph the function and find the points from there, but is there another method for finding all the points in which the function is continuous? (sketching...

I was given this problem during a quiz f(x) = tan x and i was told to find the limit as x approaches (3pi)/(2) from the positive side I'm not entirely sure if i did this problem the correct way, but I drew the graph of tan x, and i drew the point (3pi)/(2) on the x-axis, and i noticed that...

Use the intermediate value theorem to determine whether the following equation has a solution or not SquareRoot(2x) + SquareRoot(1 + x) = 4 I don't understand the formal definition of the intermediate value theorem. Can someone explain it to me in simpler terms? What am i supposed to do here?

I was given this problem.. (x - 3)/(SquareRoot(4x2 + 3)) And i was asked to find the limit as X approaches Positive infinity. I usually understand these kinds of problems, and I know i'm supposed to divide every number in the fraction by the highest degree term in the denominator. But...

For example If i am given a simple function like... f(x) = SquareRoot(x + 4) I usually just graph the function and find the range from there. Which can sometimes be a bit tedious when I am in the middle of a test. But is there a method that i can use to find the range WITHOUT graphing it?

I have been scratching my head for a couple of minutes now because of this problem. Express ln (3squareroot(32)) in terms of ln 2 and ln 3 I'm not sure how to start. I know the rules for logarithms and i've done many problems involving logs, but this one in particular is difficult. Can...

I was given this problem... What is the minimum value of f(x) = (x + 3)2 - 5 defined for all real x. A. x = -5 B. x = -3 C. x = 4 D. Not defined I'm not sure if i did this correctly, but i used all the answers and plugged them in for x in the original equation, and -3 was the minimum...

An equation of the line parallel to the line y = 2x - 3 passing through the point (k, 1) is A. y = kx - 1 B. y = 2x + 1 C. y = 2(x -k) + l D. y = (k - 2)x + (1 - 3) This stuff is usually easy for me, but the (k, 1) threw me off a bit. I think the answer is B since the rest of the option...

I was given this problem... The number pi3 - 4pi is equal to... A. pi-1 B. (pi - 2) pi (pi + 2) C. -pi It took me a while to try to solve this one, but I believe that B is the correct answer. I just used a little bit of algebra to see if I would get the same result as pi3 - 4pi Is B the...

let x > 1, the expression SquareRoot(7x4 - 7x2) is equivalent to A. SquareRoot(7x) B. SquareRoot(7x2) - SquareRoot(7x) C. 7(SquareRoot(x4 - x2)) D. SquareRoot(7x) (x2 - 1)1/2 I believe that C is the correct answer since all i need to do is multiply the 7 with x4 and x2 to get the...

I was give this problem... Solve x = (1)/(1-x) A. Solution set is empty B. x = ((SquareRoot 3) - 1)/(2) or x = ((SquareRoot 3) + 1)/(2) C. X = ((SquareRoot 5) - 1)/(2) or x = ( -(SquareRoot 5) + 1)/(2) Can someone help me solve this?

I was given this problem.. Let b3 - a3 = (b - a)(a2 + ab + b2). The inverse of 3 1/2 is given by... A. f-1 (x) = -(x+1)/(x-1) B. f(x) = (x - 1)/(x + 1) C. (a, 4) How can I begin to solve this?

I was given this problem.. Recall that (3,2). Let 7. The fraction (f(x) - f(2))/(x - 2) simplifies to... A. f(x) = (x - 1)/(x+ 1) B. x2 -2x + 4 c. 3 1/2 D. (f(x-2))/ (x - 2) This problem is a little confusing because it just tells me to "Let" 7.. What the heck does that mean? But I...

Determine for what values of t , sin t = cos t A. t = pi/4 + pi * k, where k is an integer B. no matter what value of t is, sin t is always different than cos t. C. t = pi D. t = 0 E. t = tan t I think the answer is B, since I believe that Sin and Cos will always be different. Can...

I was given this problem. Let f(x) = (1/2)x2 . The fraction (f(a + h) - f(a))/ (h) is... A. a + (1/2)h B. 1/h [(1/2)x2(a + h) - (1/2)x2(h)] C. a D. 2x E. 2a Can someone explain to me how i can begin to solve this?