Looking through my old calc notes, I am reading that f(x) needs to be continuous on [a,b] and f ' (x) also needs to be continuous on [a,b]. Both conditions are needed. If you had to pick just one, then I'd say f(x) being continuous is much more important. Though I'm not 100% sure on this one. My thinking is that if there was any discontinuities on f(x), then the arc length would be distorted and overblown. The arc length should not account for any piece that isn't on the curve.
Answer:
Step-by-step explanation:
2 * 2 = 4u² (area of the central square)
2 * 2 : 2 = 2u² (area of one congruent triangle)
4 + 2 + 2 = 8u²
(u = units)
Answer: n= -1/2
Step-by-step explanation:
Answer:
(a) There are asymptotes at x=3/2 and x=-1/3
Step-by-step explanation:
The denominator zeros can be found by factoring:
f(x) = (x +1)/((2x -3)(3x +1))
Neither of the denominator factors is cancelled by the numerator factor, so each represents a vertical asyptote, not a function hole.
The asymptotes are at the values of x where the denominator is zero:
2x -3 = 0 ⇒ x = 3/2
3x +1 = 0 ⇒ x = -1/3
Answer:
y= 5x+13
Step-by-step explanation:
<u>Slope- intercept form</u>
y= mx +b, where m is the gradient and b is the y-intercept.
Parallel lines have the same gradient.
y= 5x +4
Gradient of given line= 5
Thus, gradient of line= 5
Subst. m=5 into the equation.
y= 5x +b
To find the value of b, substitute a coordinate
When x= -2, y=3,
3= 5(-2) +b
3= -10 +b
b= 3 +10 <em>(</em><em>+</em><em>1</em><em>0</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>
b= 13
Thus, the equation of the line is y= 5x +13.
