Sketch the graph over [0, 2π]. f (θ) = sin ( 2 (θ - π/2 ) + π) + 2

Q: Q46) Use shifting graph to sketch a) y = |1 – vx|- 3 b) y = -1+ sin (x – 0.5)

A:

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = cos x −…

A:

Q: The slope of the tangent to the graph of g(x)=(6x +1)° at the point (0, 1) %3D is a) mon = 48 b) man…

A: The slope to any curve y is given by dydx at given point.

Q: Find fe F dr for F = 7yi - (sin y)j on the curve counterclockwise around the unit circle C starting…

A:

Q: * Sketch a graph of the following: TX y f(x) = - sin - * g(x) = - 0.8 cos(2x) %3D | - 27 2

A: 1.

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: For a given function f(x) the critical point are the value of x at which the derivative of f(X)…

Q: Determine the point(s) in the interval (0, 2 ∏ ) at which the graph of f (x) = 2 cos x sin 2x has a…

A: Given curve: fx=2cosx sin2x

Q: The conjugate harmonic function v(x, y) of u = In (x² + y²) is

A:

Q: Consider the graph of f(x, y) = excos(xy²). Find an equation of its tangent plane at (0,0, 1) and…

A:

Q: Find f F. dr for F = 2yi – (sin y)j on the curve counterclockwise around the unit circle C starting…

A:

Q: (a) Sketch the graph of f(t) = sin 2(t- π)U(t - π).

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: * 3x ], the x-coordinates of the points on the graph of the function f(x) = 1 + cos x where the…

A: For horizontal  tangent dy/dx=0

Q: .Is f (x) = x sinx a periodic function ? %3D

A:

Q: How does the periodicity of f (x) = sin θ and f (x) = cos θ follow from the unit circle definition?

A:

Q: Show that the p.d.f. of Z? is given by g1(x) = cosh(vAr), x > 0, wh cosh(z) = }(e² + e-=) is known…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: plot the function and use the graph to estimate the value of the limit.

A: Using the graphing utility, we get following graph of function

Q: Find the absolute maximum of the function f(x)=sin(2x)+cos(2x) on the interval [0, pi/6].

A:

Q: Prove that the inflection points of y = cos x are at the x-intercepts.

A: Inflection point

Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

A:

Q: Sketch the following curves 2. y = sin(x) + v3 cos(x) on [–27, 27].

A:

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = sin x +…

A: The given function is  f(x) = sin x + cos x on  [0, 2 ]. Compute the second derivative as follows.…

Q: Draw the following graph on the interval -315° <I < 0°: y = 3 cos(z) -300 -270 -240 -210 -180 -150…

A:

Q: Q33) Use shifting graph to sketch a) y+1 = |-3+ v2x| b) y = 2 + cos (0.1x)

A: The function translation  or transformation rules: If  y=f(x)+b then the graph shifts the function…

Q: Sketch the graph of f (x) = 3 cos (2 (x + π/2)) over [O, 2π].

A: Given: f (x) = 3 cos (2 (x + π/2)) over [O, 2π]

Q: Is the function A cos (ka - wt = psi) a function of the operators ^ E and ^ T?

A: yes this is true

Q: GIVEN: f:0,2x]- -R, f(1) = sinz+ cos I %3D Find f (x) in factored form.

A: Differentiate the function fx with respect to x.

Q: Calculate and graph the tangent of the function b) r = -6ecose + 8 cos 40 5T 0 = 4 %3D in

A: Given that, r=-6ecosθ+8cos4θ and θ=5π4

Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: Sketch the graph of f (x) = 3 cos 2x.

A: Given: y=3cos2x

Q: of the tangent line to the graph of f(x) = 7 sin(x) + 6 cos(x) at x = in the form y = mx + b.

A:

Q: 2. Consider the squiggly graph of all points (r, y) that satisfy sin(re") = a + y. 1 Using implicit…

A: Given, sinxey=x+y

Q: 15. Sketch the graphs of the following reciprocal functions. 1 1 c) y = 2* %3D Vx 1 b) y = a) y = 1…

A: The given reciprocal functions,a) y=1xb) y=1x3c) y=12xd) y=1sin x

Q: Sketch the periodic extension of the indicated function.

A: According to the given information, it is required to sketch the period extension of the indicated…

Q: Sketch the graphs of f and g in the same coordinate plane. (Include two full periods.) f(x) = 2…

A: Given, f(x)= 2cos(2x) For, x=0=&gt; y= 2cos(0)= 2  =&gt; y-intercept= (0,2) For, y=0=&gt; 2cos(2x)=0…

Q: Consider the graph of f (0) = sin(20) on the interval 0 < 0 < 2n . Find the values of 0 at which the…

A:

Q: ii. Verify that the u = -e-Y tany is harmonic in an appropriate domain D.

A: Given that u=-e-ytany.  If u is harmonic then uxx+uyy=0.

Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Q: Let a function y(x) be given implicitly by the formula: y° - 3xy2 +y cos(x) – x = 10. %3D Find the…

A:

Q: Find the lengthof the curve r= a sin² (0/2), 0 s0s T, a>0

A:

Q: The graph of f(t) = tan (2t + 4T) intersects the t axis on the interval [0, TT] at points %3D

A: Graph of the function f(t) intersects t axis when f(t) becomes zero. Substitution of f(t) by zero…

Q: Find an equation for the tangent line to the graph of f(x) = -2x2 + 2x + 3 at the point where x = 1…

A:

Q: h) = 3 sin h (1-3x) cosh (1-3)

A: Given that hx=3sinh1-3x2cosh1-3x2 The objective is to find the derivative for h(x). The facts used…

Q: Find and sketch the domain for the function. cos (xy) f(x,y) = 2 x² + y²-81

A: The given function,  f(x,y)=cosxyx2+y2-81

Q: Let z be a function of x and y implicitly defined by the equation xye" – In (x² + y) = sin(x-z2) i)…

A:

Q: Sketch the graphs of y= f(x) and y=- given that: f(x) f(x)=4x² –1 - a b f(x)=sin(x)+1 given 0<x<2n“

A: Given function is   a. f(x)=4x2-1   b. f(x)=sinx+1 , [0,2π]

Q: Verify whether the function u=e^(x^2-y^2 ) cos⁡2xy is harmonic or not.

A: A function u=fx,y is said to be harmonic if ∂2u∂x2+∂2u∂y2=0 Now, we have u=ex2-y2cos2xy We will use…

Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: