For f(x) = x − 4 1 + x 2 + tan−1 x, find all characteristics listed below. Do not find the x-intercepts or check for symmetry. Approximations of answers may be used as needed. If any of the characteristics are not present in the function, state NONE. Then, using these characteristics, sketch the curve Domain: y-intercept: V.A: H.A/S.A:
Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
For f(x) = x − 4 1 + x 2 + tan−1 x, find all characteristics listed below. Do not find the x-intercepts or check for symmetry. Approximations of answers may be used as needed. If any of the characteristics are not present in the function, state NONE. Then, using these characteristics, sketch the curve
Domain:
y-intercept:
V.A:
H.A/S.A:
Inc:
Dec: Loc. Max:
Loc. Min:
Concave up:
Concave down:
Inflection points:
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Given,
a)Domain:
The domain is the input value of the function that is the value of x.
Domain=
b)Y-intercept:
To find y-intercept put x=0 in the given function we get,
Therefore y-intercept is
c)Vertical asymptotes:
Vertical asymptotes are the vertical line that corresponds to zero of the denominator of the rational function.
Given function,
we have to plug the value of the denominator equal to zero.
But here we don't have any denominator,
So the function doesn't have any vertical asymptotes.
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