Using tangent fins to derive the length formula for curves As-sume that f is smooth on [a, b] and partition the interval [a, b]in the usual way. In each subinterval [x-1, X], construct the tan-gent fin at the point (xx-1, f(xk-1)), as shown in the accompanyingfigure.a. Show that the length of the kth tangent fin over the interval[xx-1, x] equals V(Ax,)* + (f'(x}–1) Ax4).b. Show that(length of kth tangent fin)VI + (f'x))² dx,lima

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Answered: Using tangent fins to derive the length…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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a) Use the reduction formula twice to find the value of this integral: integral tan^(5)xdx Reduction formula:integral tan^(m)xdx=(tan^(m-1)x)/m-1 - integral tan^(m-2)xdx. b) Use the Product to Sum Identities and integration to find the Area of the Q1 region trapped between the graph of the function f(x) and the x – axis over the given interval. Sketch the region first and estimate its’ size before integrating in each case. 1) f(x)=4sin(3x)cosx, I: [0, pi/3] 2) f(x)= 6cos(2x)cosx, I: [0, pi/4]
Sketch the graph of a function ƒ that is concave up on aninterval containing the point a. Sketch the linear approximation to ƒ at a. Isthe graph of the linear approximation above or below the graph of ƒ?
Using the residue theorem, evaluate the integral Show the details of your calculation clearly. Provide a sketch of your contour of choice (including the relevant singular point(s)) and check that the conditions for Jordan’s lemma to hold are satisfied before invoking the lemma.
Determine whether the function is continuous over the interval (negative 6−6,66)? -6-4-2246-2246xy A coordinate plane has a horizontal x-axis labeled from negative 6 to 6 in increments of 1 and a vertical y-axis labeled from negative 2 to 6 in increments of 1. A curve falls shallowly, passes through the point (negative 1, 1.4), and then falls steeply to (1, 0). It then rises steeply from (1, 0), and then rises more shallowly as it passes through (3, 1.4). An open circle is plotted on the curve at (3, 1.4). All coordinates are approximate. Is the function continuous over the interval (negative 6−6,66)?
Using riemann sums, determine the area bounded by the function f(x)=(2x^2) +1 in [3,5]. Make the graph
Approximate the area under fx)=x^2 from x=1 to x=4 using four rectangles and a right approximation (right endpoint Riemann sum). Make a sketch of what the graph and the four rectangles look like. Most important part is the sketch. hint: This question is much easier with fractions
Find the area (in square units) of the region under the graph of the function f on the interval [1, 5], using the Fundamental Theorem of Calculus. Then verify your result using geometry. f(x) = -1/5x+1 (negative one fifth) _______ square units
Let f(x)= tan(x∕10) for 2π≤x≤3π. We want to estimate *Attached by the midpoint method. In (a), (b) and (c), you must give the exact values (in the form of formulas). Approximate decimal values are not accepted.a) Divide the domain of f into 5 subintervals of the same length. Calculate their common length Δx b) What are the midpoints m1, m2, m3, m4 and m5? List their values below, in ascending order, separated by commas. c) List the corresponding values f(m1), f(m2), f(m3), f(m4) and f(m5) below, separated by commas. d) Using the information found in (a), (b) and (c), determine the approximation of *Attached provided by the midpoint method with 5 sub-intervals. Give the answer to 3 decimal places.
For the function given below, find a formula for the Riemann sum obtained by dividing the interval [a b] into n equal subintervals and using the right-hand endpoint for each c. Then take a limit of this sum as n oo to calculate the area under the curve over [a,b] f(x)=x+5x² over the interval [0,1]. Find a formula for the Riemann sum. Sn= The area under the curve over [0,1] is square units (Simplify your answer.)
For the function given below, find a formula for the Riemann sum obtained by dividing the interval [0.6] into n equal subintervals and using the right-hand endpoint for each c. Then take a limit of this sum as n oo to calculate the area under the curve over [0,6]. f(x) = 36-x2 Write a formula for a Riemann sum for the function f(x)=36-x over the interval [0.6] S.- (Type an expression using in as the variable.) The area under the curve over [06] is square units (Simplify your answer.)
Is the proof correct? Either state that it is, or circle the first error and explain what is incorrect about it. If the proof is not correct, can it be fixed to prove the claim true? Claim:If f : [a, b] → R is continuous and not constant, then its range is a closed, bounded interval. Proof: Since f is continuous on a compact domain, its range is compact and hence closed and bounded. Since the range is bounded, it has a supremum and an infimum.Since the range is also closed, the supremum and infimum belong to the range. Therefore the range is the closed and bounded interval [m,M], where m is the infimum and M is the supremum of the range.
(a)Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using fiveapproximating rectangles and right endpoints. Sketch the graph and the rectangles. Repeat part (a) using left endpoints

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