If in the real number universe, first k is to be >0, y=kx = exlog(k)
the antiderivative of eax is eax/a so the antiderivative of Y
is exlog(k) / log(k) = kx /log(k)
if f(x)=kx, f'(x)=ln(k)*kx. Therefore, the derivative of 2x is ln(2)*2x.
k + 5k = 6k 2 x 3 x k
4x-9=k 4x=k+9 Divide by 4 to isolate the x x=(1/4)k+(9/4) x=1/4 k+ 9/4
x = ¼x^4 + 4x + k where k can be any number
Yes, if you accept that the definition of the exponential function f is given by the two statements (1) f(0)=1, and (2) f'(x)=f(x) for all real x, then you have from differential equations that the function is represented by a power series $f(x)=sum_{k=0}^\infty \frac{x^k}{k!}$. If you accept that this means that f(x) is everywhere positive, then you have that f is monotone (increasing), which implies that it is one-to-one by the mean value theorem.
racist
Let X have a Poisson distribution.Therefore Pr(X=x) = e^(-k) * k^x/x! where x = 0, 1, 2, ...Normally the parameter is the Greek letter, lambda, but this site does not allow any such symbols!Then the moment generating function of the Poisson distribution isE[exp(tx)] = Sum[e^(tx)*Pr(X=x)] where the sum is over all non-negative integers, x.= Sum[e^tx * e^(-k) * k^x/x!]= Sum[(e^t)^x * e^(-k) * k^x/x!]= e^(-k) * Sum[(e^t)^x * k^x/x!]= e^(-k) * Sum[(k*e^t)^x /x!]= e^(-k) * e^(k*e^t)= e^[k*(e^t - 1)]
No, the sum of two power functions is not always a power function. For example, if we take ( f(x) = x^2 ) and ( g(x) = x^3 ), their sum ( f(x) + g(x) = x^2 + x^3 ) is not a power function, as it cannot be expressed in the form ( x^k ) for a single exponent ( k ). In general, the sum of two power functions with different exponents yields a polynomial rather than a single power function.
To model a situation where ( y ) varies inversely with the fourth power of ( x ), you can use the equation ( y = \frac{k}{x^4} ), where ( k ) is a constant. This means that as ( x ) increases, ( y ) decreases in proportion to the fourth power of ( x ), and vice versa. The constant ( k ) can be determined based on specific conditions or data points related to the situation.
Factor them. k2 = k x k k2 - 1 = (k - 1)(k + 1) k2 - 2k + 1 = (k - 1)(k - 1) Combine the factors, eliminating duplicates. k2(k + 1)(k - 1)(k - 1) = k5 - k4 - k3 + k2, the LCM
k = x y x = k/y
if f(x)=kx, f'(x)=ln(k)*kx. Therefore, the derivative of 2x is ln(2)*2x.
k and -k right? -k x -1 =k k+k= 2 k= 1 unless you mean multiply then that would be -k x-1 =k k x k= 2 1.4142 rounded to the nearest ten thousandth
Use the formula: power = voltage x current x power factor If you don't know the power factor, assume it is 1 - this is close enough for many devices. In units: power (in watts) = voltage (in volts) x current (in amperes)
The area under a curve (ie between the curve and the x-axis) is found by integrating the curve with respect to x: A = ∫ y dx When limits to the integration are given, then the value of the area is the difference between the value of the integral at the limits. The lower limit is where the curve y = √x meets the x-axis, ie at y = 0 → √x = 0 → x = 0 The upper limit is the line x = k → the area is given by ∫ √x dx between 0 and k To integrate √x write it in power format: √x = x^½, giving: ∫ √x dx = ∫ x^½ dx = ⅔x^(3/2) + c The difference between the limits is the area: (⅔k^(3/2) + c) - (⅔0^(3/2) + c) = 18 → ⅔k^(3/2) = 18 → k^(3/2) = 18 ÷ ⅔ = 27 → k = 27^(2/3) = (27^⅓)² = 9 Thus k = 9.
K-x. In red!
∫ 10x dx Factor out the constant: 10 ∫ x dx Therefore, by the power rule, we obtain: 10x(1 + 1)/(1 + 1) + k = 10x²/2 + k = 5x² + k