Calculus Calculus Math Forum

 February 11th, 2016, 04:14 AM #1 Newbie   Joined: Feb 2016 From: hk Posts: 1 Thanks: 0 please help!!exam is coming!!!!! Please evaluate the following limit(if exits) I am going to have exam next month and I am struggling with some past exam paper and I figure out there are many questions I have no ideas to deal with.Please help me and show the steps..... I know there are lots of questions but I really hope that if you could spend few minutes to solve for me and I am sure that it will help me to have a great improve before exam. 1.)given that cschx=-9/40, find the value of coshx and tanhx 2.)lim x-->9 (x(sqrt(3) - 3)) / (x - 9) 3.)lim x-->-infinity x^(1/3)-5x+3/2x+x^2/3-4 4.)lim x-->0 1-cos(ax)/x^2,a not equal to 0 5.)lim x-->+infinity (3+2/x)(cos 1/x) 6.)lim x-->+infinity (sqrt(x^2+x)- sqrt(x^2-cx), where c is a positive constant 7.) let f be a function that satisfies |f(x)| <=M for all x is not equal to 0 Show that lim x-->0 (x*f(x))=0. 8.)Suppose that f is differentiable at x, show that f'(x)=lim delta x-->0 f(x+deltax)-f(x-deltax)/2*deltax 9.)Find the derivative dy/dx: i) 3y^3-4x^2y+xy=-5 ii)y^3+sinhxy^2=3/2 10.) It is given that e^xy=x[(x+1)^]3/(x^2+1) ,where x>0
 February 11th, 2016, 06:15 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond You've posted ten questions without showing any effort towards solving them. Us doing your studying for you is not going to help. Can you make an effort to solve them and post where you are having difficulty? Thanks from topsquark
 February 11th, 2016, 05:47 PM #3 Senior Member   Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics Also, it would be great if you could use $\displaystyle \LaTeX$
 February 12th, 2016, 03:39 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Do you know the standard identities for the hyperbolic functions? The basic one is $\cosh^2(x)- \sinh^2(x)= 1$. What do you get if you divide both sides of that by $\cosh^2(x)$? Last edited by greg1313; February 12th, 2016 at 05:35 AM.
 February 12th, 2016, 06:34 AM #5 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 The second question seems diverges for me.

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### f(x deltax)-f(x)/delta x 1/x^2

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