b) Evaluate y at position r = 0.5. c) dy * at position a = 0.5. da Evaluate the derivative

Q: 6. Find the length of the curve r = 1+ cose

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Q: a) Use Newton's Method to find an approximation of: accurate to within 10-3 V5+1

A: First we will obtain the equation which will have the value    as its root. then we will obtain the…

Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…

A: We find the point of intersection by setting them equal

Q: d all points on the graph of the function f(I) = 2 sin z + sin z, 0 <I< 27 at which the tangent line…

A: Given query is to find the points where tangent is horizontal.

Q: Use Newton’s method to approximate, to within 10−4, the value of x that produces the point on the…

A: Given: y=1x and sme point 2,1

Q: The exact value of the slope of the tangent line to the graph of the curve r = 9 + 8 cos(e), at e =…

A:

Q: Use Newton’s method to approximate all the intersection points of the following pairs of curves.…

A:

Q: bounded by the curve y=tan7 Y: Generate by revolving the regioh and X: - chont the about the Y-axis-…

A: Given, The curves are :                     .

Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26p units along the…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate 3.6^7 as follows: Let f(x)=x^7. The…

A:

Q: 3. Use linear approximation, i.e. the tangent line, to approximate 6.9 as follows: Let f(z) = r. The…

A:

Q: Consider the function y = f (x) = x² + 10 + 24 and the x-value xo = 5. %3D %3D (a) Find a formula…

A:

Q: The tangent line to the graph of y = e² at æ = 0 is perpendicular to the tangent line to y = e at æ…

A:

Q: written

A:

Q: Find the length of the curve y = ln(sec x ), x is an element of [0, pi/4]

A:

Q: Find the area bounded by the trigonometric curves O2.828 square units 1.414 square units 3.667…

A: To find: To find the area bounded by the trigonometric curves- y=sin x and y=cos x from x=π4 to…

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: A ladder 22 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A: here need to find the relation between x and y using pythagorean theorm. the solution is following.

Q: Consider f(x)=tanx a. Find the linear approximation of f(x) at a=pi/4 b. Use this to estimate…

A: This question can be solved using the formula of linear approximation.

Q: Use linear approximation, i.e. the tangent line, to approximate 3.6° as follows: Let f(z) = a. The…

A:

Q: (a) What is the derivative of sin t? d sin t dt (b) The velocity of a particle at time t is v(t) =…

A: (a) From the given problem:   ft=sint   So,   dftdt=ddtsint=cost...we know that:dsinxdx=cosx   Hence…

Q: Use linear approximation, i.e. the tangent line, to approximate 1 as follows: 0.252

A:

Q: Using Trapezoidal Rule, with n = 10, approximate the ntegral below. Give the error of approximation…

A: To solve the following problem using trapezoidal rule

Q: 3 dz using the midpoint rule with three subdivisions to four decimal In(x) 1 Approximate places. The…

A: We will proceed as follows

Q: Use linear approximation, i.e. the tangent line, to approximate 3.6° as follows: Let f(x) = x°. The…

A:

Q: Q: Find the condition that the line x cos a +y sin a = p may touch the curve x"y" = a™*".

A: Answer

Q: Use Gaussian Quadrature of order 5 to approximate 08 6 2 x-1 To how many decimal places is this…

A: Given that,    f(x)=∫286x-1dx                                  1 Using the Numerical Integral by…

Q: Q: Prove that the arc lenfth af Curve y = log secx from to n- 3 is Use formula Note I+ ( dn.

A: Given: y = log sec x To prove: The arc length of the function y from x = 0 to is .

Q: Use linear approximation, i.e. the tangent line, to approximate 1.9² as follows: Let f(x) = x². The…

A:

Q: The surface of a water wave is describedby y = 5(1 + cos x), for -∏ ≤ x ≤∏, where y = 0corresponds…

A: Given- y=51+cosx and consider the figure, To find- The average height of the wave above the trough…

Q: 1.) The slope of the tangent line to the wve y?= 5+-1 at PCi,e) 2.) Find the First denivative of…

A: Using derivatives.

Q: use taylors formula to find the cubic approximation to f(x,y)=sin(6x+y) near the origin

A: Given Function,fx, y = sin 6x + y

Q: 3. Find a positive root of cosx - xex = 0 upto four decimal places, using Newton-Raphson mehtod. %3D

A: I am attaching image so that you understand each and every step.

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: ind the length of arc of the curve 6xy = x⁴ + 3, from the point where x = 1 to the point where x =…

A: Here given equation as 6xy=x4+3ory=16x3+3x Differentiate with respect to x…

Q: Q1. By using cubic approximation of Langrange Interpolation, approximate f(7.65) based on the…

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 ex cos (yz),…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate 2.8* as follows: Let f(x) = x*. The…

A:

Q: Find the interval on which the curve 1 dt 6 +t + 2t2 y = is concave upward. Note: When using…

A:

Q: Use linear approximation to approximate√25.4 as follows. Let √f(x)=x. The equation of the tangent…

A:

Q: Find the points on the interval -n s0s n at which the cardioid r = 1- cos(0) has a vertical or…

A:

Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table.…

A:

Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

Q: Find the arc length of the curve below on the given interval. y = In (x-√x² - 1), for 1 ≤x≤ √442…

A: Given y=lnx-x2-1, for 1≤x≤442   To Find: The arc length of the curve given on the given interval.

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0sos…

A:

Q: the derivative of the function f(x,y) = - 4xy – 4y², Po(10, PA) (10.- 7) =0 (10, – 7) Type an exact…

A: Given: f(x,y)=-4xy-4y2 And A=4i-2j

Q: Use linear approximation, i.e. the tangent line, to approximate 1.06 as follows. Let f(æ) = VT and…

A: Solve the following

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 e* cos (yz),…

A: We can solve this as follows:

Q: that cos (x-T) 2/a Find the puints on the curve y= 2x-3x-12.X + 20, where the tangent is parallel to…

A: