Let f : [a, b] → r be a continuous function. let ε > 0 be a constant. for x ∈ [a+ε,b−ε], define g(x) : = 1 2ε z x+ε x−ε f.
a) show that g is differentiable and find the derivative.
b) let f be differentiable and fix x ∈ (a, b) (let ε be small enough). what happens to g 0 (x) as ε gets smaller?
c) find g for f(x) : = |x|, ε = 1 (you can assume [a, b] is large enough).

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?

a

step-by-step explanation:

25/6

step-by-step explanation:

you multiply 4 by the denominator (4*6=24) and add it to the numerator which makes it 25/6.

the area of a triangle is determined by the formula: base x height * 1/2

you'll need to assign a base to the triangle. based on the vertices given, the simplest base would be the line segment from (-2,1) to (2,1). the distance between any two numbers is found by just subtracting them. here, you should subtract the x values to find the distance of this side.

2 - (-2) = 4.

so the distance (aka the length of the base) is 4. the height of the triangle is the distance between the base and the highest point on the triangle which is (3,4). we should subtract the y values this time to find the height/distance.

4 - 1 = 3

so the height is 3.

base = 4

height = 3

hope this if needed hmu