Mathematics

How to find the inverse of the function e^sqrt(x)

How to find the inverse of the function e^sqrt(x)? the answer is (lnx)^2 is there a way to find it on the gdc ?-x = e^(sqrt y) ---> sqrt y = ln x ---> y = (ln x)^2-O.O I think my brain just leaked ou

What is the integration of (x+1/sqrt(x) ) ^2

What is the integration of (x+(1/sqrt(x)) ) ^2?-Ans: (x+1/sqrt(x) ) ^2 = x^2 + 2sqrt(x) + 1/xhence the integral is = (x^3)/3 + 4/3(x^(3/2)) + ln(x) + c-Its easiest to just expand: = x^2 + 2sqrtx + 1/

Differentiation: A sign question.

It was a longer question but one part involved me differentiating: -2xy. I took this to be -2x(dy/dx) -2y, but the mark-scheme says its -2x(dy/dx) + 2y. Why is it +2y??-x^3 − 2xy − 4x + y^3 − 51 = 0

How do you solve this A level maths solid of revolution question

I did a past paper and got part b of question 2 wrong. Here is the link to the paper: http://www.carlgauss.co.uk/PDFs/A-Level%… I found the answer to 2a to be pi/12 Heres the mark scheme if that helps

How am i to solve limθ➝π⁄₃ (2cosθ -1)/(θ - π⁄₃) without using the L'Hôpital's Rule

Please write the steps out. The answer should be -√3 right?-Put z = θ–π/3 and let L = lim [θ→π/3] {2cos(θ)−1}/(θ–π/3) 2cos(θ) – 1 = 2cos(z)cos(π/3) – 2sin(z)sin(π/3) − 1 = cos(z) − 1 − √3.sin(z) =

Help with this word problem

Jane filled her beaker with 40ml of a 75% solution of hydrochloric acid. Her chemistry teacher pointed out that she should have 40 ml of a 50% hydrochloric acid solution. Jane drains x ml from her bea

Determine the equation of the Parabola

Determine the equation of the Parabola with the following: The x-intercepts are -4 and 3, and the curve passes through the point (2,7) Could you also explain how you got this? Thanks!-The x-intercep

Simplify the square roots

square root of 12 square root of 48 square root of 4/16 4/square root of 5-Sqrt[12]=Sqrt[4*3]=2 Sqrt[3] Sqrt[48]=Sqrt[16*3]=4 Sqrt[3] Sqrt[4/16]=2/4=1/2 4*Sqrt[5]/(Sqrt[5]*Sqrt[5])=4/5 * Sqrt[5]-squar

Solving Eqautions and Factoring

Solve Equations x sqaured + 5x + 6=0 3x-7x sqaured = 0 Factoring 4x sqaured - 4x-3 (x+4) (x+6)+ ( x-9) (6-x)-1.) x²+5x+6 = 0 (x+2)(x+3) = 0 x+2 = 0 or x+3 = 0 x = -2 or x = -3 Solutions: x =

Can some one check my algebra answers for these two questions

1)Find the domain and range of: a) g(x)=I2x-3I-3 b) h(x)=3x+2/x-1 c) f(x)=x^4-4 Answer a)domain=all real numbers range= all real numbersb)domain=(negative infinity,1)u(1, positive infinity) range=(neg

Square root questions

1. What is the product of 4 square root of 6k * 3k square root of 3 2. What is the product ofsquare root of t (8-3) square root of 5 3.What is the product ofsquare root of 3 (2b square root of 49

I need help with a matrix problem. Question is in additional details.

Amanda, Bryce, and Corey enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Corey finishes first with a total time of 1 hr 41 mi

Can -5 be the square root of 25

well, my mum and I have been arguing about this matter. SO - can -5 be considered the square root of 25? -5^2 = 25 please answer quickly!-You and your mom are BOTH right! You can say that 5 is a squ

How do you prove whether a set of polynomials is in the vector space P³

This may not be all that helpful, but you must prove the 10 axioms of a vector space using what you are given. 1. For all x,ycontained in V, then x + y is contained in V. (closure under addition) 2.

Use of Taylor's formula

Could anyone please help me with the following two problems? 1). f(x)=1/(1+x^3), determine f^100(0) (The 100th derivative at x=0.) 2). Find using Taylors formula lim(x→0)(sinx-x)/(x(1-cosx)) Thanks