the graph of f a) Evaluate  the integral from 1 to 9 of f(x) dx           (b) Determine the average value of f on the interval  [1, 9].

Q: Find an equation of the tangent line to the curve at the given point. y = In(x2 - 8x + 1), (8, 0) y…

A:

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: Use the graph of f'  shown in the figure (see the figure as attached here ). to answer the following…

A: Given :              The graph of                               f(x) = 5x3+10x(x2+1)2

Q: Differentiate the function f(t) = t^3 − it^2 when t = 2

A: Here, f(t)=t3-it2⇒f'(t)=3t2-i(2t)⇒f'(t)=3t2-2ti

Q: Is this function analytic fizz=. (1 +x)? +y2 2

A:

Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, f(5) = 0 f(x) =

A:

Q: Differentiate the function. h(t) = √t-8e* h'(t)

A:

Q: Find the average rate of change of the function f(x)=x^3over the interval [1,1+h]. Simplify your…

A:

Q: /Sketch the Function Y=Sgn(x) + Sgn (x-) and Finat its domain and vang es

A:

Q: Explain geometrically how the Midpoint Rule is used to approximate a definite integral.

A: Concept: Calculus helps in understanding the changes between values that are related by a function.…

Q: Using four triangles to estimate the area under f(x) is approximately

A:

Q: Use secant method to estimate a root for function f(x)= x3 + 2.7x+ 2.6 = 0, starting for interval…

A:

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

A: It is given that f''(a)=0 at (a, f(a)). The objective is to explain and sketch how a function can…

Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, f(7) = 0 f(x) =

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.