(i+1)^

**k**= -(3^**k**) => ((1+i)/3)^**k**= -1 => ln[((1+i)/3)^**k**] = ln(-1) =>**k**ln((1+i)/3) = ln(-1) =>**k**[ (1/2...**k**/2) and the abs. v. of the right side is 3^**k**, and a power of 3 cannot be equal to a power of...2 Answers · Science & Mathematics · 06/05/2013

**k**^2 - 4k - 12 > 0**k**^2 - 6k + 2k - 12 > 0**k**(**k**- 6) + 2 (**k**- 6) > 0 (**k**- 6) (**k**+ 2) >...you can get a product greater than 0. So EITHER**k**- 6 > 0 AND**k**+ 2 > 0 (both factors are positive...1 Answers · Science & Mathematics · 22/01/2009

**k**^2 - 3k = 28**k**^2 - 3k - 28 = 0 (**k**- 7)(**k**+ 4) = 0**k**= -4, 7 and if you're asked to find x:**k**= -4: -4 = (x + 3)/(x - 4) -4(x - 4) = x + 3 -4x + 16 = x + 3 16 - 3 = x...2 Answers · Science & Mathematics · 18/08/2019

I assume you need to find

**k**so that this function is continuous at x = -2. We need to show that lim...2+) f(x) = lim (x->-2-) f(x) lim (x->-2+) (1/2)kx = lim (x->-2-) (2x^2 +**k**) (1/2)(-2)**k**= 2(-2)^2 +**k**-**k**= 8 +**k**-2k = 8**k**= -4 Then lim (x->...1 Answers · Science & Mathematics · 14/07/2011

Question

**K**-Form (Precalc/Calculus)? The directions...6k ((((THIS 6k SHOULD BE 2k(pi) )))) 2x=(5pi)/6 + 2k(pi)**k**= 0,1 x= pi/12 +**k**(pi) x=(5pi)/12 +**k**(pi) x= pi=12, 13(pi)/12, 5(pi)/12, 17(pi...1 Answers · Science & Mathematics · 07/12/2008

(h,

**k**) Explanation: y = a*(x – h)^2 +**k**If x = h, then y = a*(h – h)^2 +**k**y = a*(0)^2 +**k**...a > 0 i.e. the parabola has upward orientation, then a +**k**>**k**. Therefore, y =**k**is the lowest...3 Answers · Science & Mathematics · 08/06/2011

...e^(

**k**x) - e^(-**k**x) ] / [ e^(3x) + e^(-3x) ] When x is large and assume**k**>= 0 sinh(**k**x) / cosh(3x) ≈ e^(**k**x) / e^(3x) = e^(x(**k**- 3)) For sinh(**k**x...1 Answers · Science & Mathematics · 21/02/2019

[-

**k**+/- SQRT (**k**^2 - 4)] / 2 Since this equation opens up, the vertex...to never cross the x-axis, then it must have imaginary roots. So.. when**k**^2 - 4 < 0 So,**k**must be between -2 and 21 Answers · Science & Mathematics · 21/04/2007

Suppose

**K**is not compact. Then, by Heine Borel theorem,**K**...since**K**is unbounded, for every M > 0 there is x ∈**K**such that f(x) = ||x|| > M, which shows f is a continuous unbounded...2 Answers · Science & Mathematics · 04/07/2010

If

**k**= 1, then this series diverges by the nth term test, because lim(n→∞) n! = ∞. ---------- Assuming**k**> 1, now we use the Ratio Test: r = lim(n→∞) [((n+1)!)^2 / (**k**...1 Answers · Science & Mathematics · 07/04/2013