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Sep 23, 2017 · Yes, but also see below ln^2 x is simply another way of writing (lnx)^2 and so they are equivalent. However, these should not be confused with ln x^2 which is equal to 2lnx There is only one condition where ln^2 x = ln x^2 set out below. ln^2 x = ln x^2 -> (lnx)^2 = 2lnx :. lnx * lnx = 2lnx Since lnx !=0 lnx * cancel lnx = 2 * cancel lnx lnx = 2 x =e^2 Hence, ln^2 x = ln x^2 is only true for x=e^2
Jun 30, 2017 · 2lnx ⋅ (1 x) = 0. Since 1 x ≠ 0 → 2lnx = 0. 2lnx = 0 → x = 1. Hence f (x) has a turning point at x = 1. f (1) = (ln1)2 = 0. Since f (x) ≥ 0 → f (1) = f min. ∴ f min = 0 at x = 1. We can see these results on the graph of f (x) below. graph { (lnx)^2 [-10, 10, -5, 5]}
Jul 7, 2015 · This is known as a difference of squares. It can be factored as: x^2 - y^2 = (x-y) (x+y) Notice that when you multiply (x-y) by (x+y) then the terms in xy cancel out, leaving x^2-y^2 ... (x-y) (x+y) = x^2+xy-yx-y^2 = x^2+xy-xy-y^2 = x^2-y^2 In general, if you spot something in the form a^2-b^2 then it can be factored as (a-b) (a+b) For example ...
May 31, 2015 · The term 'the square root of X' is not quite precise as there are usually 2 square roots called sqrt (X) and -sqrt (X) sqrt (x^2) = abs (x) This is the positive square root of x^2. -sqrt (x^2) = -abs (x) is also a square root of x^2 It's tempting to say sqrt (x^2) = x, but that's only true for x>=0.
Feb 9, 2017 · What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question
Mar 9, 2017 · See below: Let's take a quick example and see why sqrt(x^2)=absx and not simply x. Let's set x=3,-3 and put them into the sqrt(x^2) term: x=3=>sqrt(x^2)=>sqrt(3^2)=sqrt9=? x=-3=>sqrt(x^2)=>sqrt((-3)^2)=sqrt9=? What should be in the question mark spaces? In both these cases, we can end up with the original value of x, but we can also end up with the opposite sign, or -x. Our general formula ...
The Trigonometric Identities are equations that are true for Right Angled Triangles. Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2π while tangent and cotangent have period π. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions.
Sep 7, 2015 · Using the Pythagorean identity: tan^2x = sec^2x - 1 This is an application of the Pythagorean identities, namely: 1 + tan^2x = sec^2x This can be derived from the standard Pythagorean identity by dividing everything by cos^2x, like so: cos^2x + sin^2x = 1 cos^2x/cos^2x + sin^2x/cos^2x = 1/cos^2x 1 + tan^2x = sec^2x From this identity, we can rearrange the terms to arrive at the answer to your ...
Sep 19, 2015 · Explanation: This is the same as the normal cos where the negative bits became positive because of the square: Graphically: Answer link. iOS. Android.
Explanation: The discriminant indicated normally by #Delta#, is a part of the quadratic formula used to solve second degree equations. Given a second degree equation in the general form: #ax^2+bx+c=0# the discriminant is: #Delta=b^2-4ac#. The discriminant can be used to characterize the solutions of the equation as: 1) #Delta>0# two separate ...
