What is the value of limθ→0 ((sin θ)/θ)? Does it matter whether u is measured in degrees or radians? Explain.

Q: If f(w) = sin(4w), find f'(w). Use exact values. %3D

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Q: Use the trapezoidal rule with n = 4 to approximate cos(x) dx finel

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Q: Find the length of the arc y = In(cos x) between the points (0, 0) and (pi/3, -In2).

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Q: Use the Fundamental Theorem of Calculus to find (2 + cos x) dx.

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Q: Because f(t) = sin t and g(t) = tan t are odd functions, what can be said about the function h(t) =…

A: Given functions are: f(t) =  sin t g(t) = tan t Since we have, f(-t) = sin (-t) = - sin t = - f(t)…

Q: Evaluate using Theorem 2 as necessary.

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Q: Find the tangent of KJ. E H G tan (J)

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Q: Determine whether the statement (d/dx) [arctan(tan x)] = 1 for all x in the domain. is true or…

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Q: The circles r = sqrt(3) cos u and r = sin u intersect at the point (sqrt(3)/2, pai/3). Show that…

A: For r=sqrt(3)cos(theta) find dr/d theta

Q: Which of the following functions is homogeneou x sin y + y sinæ A В x3 + y? æe/2 + ye*/y arcsin(xy)…

A: We check the which of the following given equation is homogeneous. A. xsiny+ysinx   B.x3+y2 C.…

Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: Let y = tan10 (x5).Find ƒ, g, and h such that y = ƒ(u),where u = g(v) and v = h(x).

A: The given function is

Q: Find the circumference of the curves x=e^-2θ (sinθ+cosθ), y=e^-2θ (sinθ-cosθ) over the interval 0 ≤…

A: To find: The circumference of the given curves. Given information: Concept used: If a functions are…

Q: Find an interval of t-values such that c(t) = (cos t, sin t) traces the upper half of the unit…

A: Interval.

Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

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

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Q: Find the limit of the trigonometric function.

A: The given expression is limx→06-6cosx3

Q: a) cosh (x) tanh' (?) = sech'! (?) find the "(?) " %3D %3D b) ln () = ? --

A: We are given : cosh-1(x)=tanh-1?=sech-1(?) Let,   Now, cosh-1(x)=tanh-1t=sech-1(y) Taking…

Q: If y = arctan x, then what restriction is placed on the value of y?

A: Consider the given function:  y=arctanxDomain of  arctanx:  −∞ <x<∞Range of arctanx:…

Q: What is the length of arc XY? 45

A: Arc Length Theorem:         The length of an arc of a circle is product of  a ratio measure of the…

Q: Describe with a sketch the end behavior of f(x) = cos x.

A: Given:            f(x) = cos x  The cosine function oscillates between values -1, 1 as x→∞ Hence it…

Q: Use symmetry to evaluate the followingintegrals.

A: Given:∫-11 1-x dxIf f is an odd function f-x=-fx∫-aa fx dx=0If f is an even function f-x=fx∫-aafx…

Q: Find the values of a and b such that

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Q: of Use the definiion Çaplace to determine the fessz e

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Q: Suppose that f'is continubus, f(o)-o and f(5)= e So f'(x) sin?Cf(x) dx 4) Calculate

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Q: What is the definition and formula for arc length?

A: The arc length is the measure of the distance along an arc in a circle. The length of arc is…

Q: What is the trigonometric substitution that you would use to evaluate the integral S V5x2 + 10x +…

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Q: Give an example to justify that sin (A + B) is not equal to sin A + sin B. Limit A and B to special…

A: Special angles are those angles at which the values of the trigonometric ratios are known. For…

Q: a. Use the definition of the derivative and the identity sin(a + B) = sin(a) cos(B) + cos(a) sin(B)…

A: As per Bartleby guidelines, for more than one questions asked, only one is to be answered. Please…

Q: Find the limit of the trigonometric function. (If an answer does not exist, enter D cos(20) tan(20)…

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Q: Use the mean value theorem to show that |sin a – sin b| < |a real values of a and b where a + b

A: let f(x)= sin x f is continuous  on [a,b] and differentiable  on (a,b) Therefore there exist  c such…

Q: Consider the function defined by f(z) = sin z cos 3z. Find f" () Give an exact answer.

A: We know that, product rule of differentiation states that ddxfx·gx=fx·g'x+gx·f'x            ⋯⋯1 We…

Q: find the arc lenght of f(x)= ln(cos x) on [pi/4, pi/3]

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Q: Find the arclength of y = 2x? +1 on 0 < x < 4

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Q: Sketch the following, marking points of interest. Y = (*+2}(x+4}/(x+3) Y= 2 sin x+1 Y= sin (2x)

A: Given Y = (x+2)(x+4)/(x+3) Y = 2sinx+1 Y=sin(2x)

Q: ind all the tangents to the curve y cos (x %3D

A: Here we have to find the tangents on the curve y=cos(x+y)...........(1)     , -2π≤x≤2π parallel to…

Q: Express x and y in terms of trigonometric Patlos of X = y = P Type here to search

A: Use trigonometric ratio to solve

Q: t+1 e i+ sin 2t lim 花1=?

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Q: Find the are of the sector on the specified interval  r= sqrt*tan theta  0 less than equal to theta…

A: Find the area

Q: Use the Second Fundamental Theorem of Calculus to evaluate cos (E) dx.

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Q: Find the tangent of ZH. H. Write your answer as an integer or as a decimal rounded to the nearest…

A: We know that tangent of an angle is a ratio of opposite side to adjacent side.

Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

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Q: Evaluate lim i+ cos rj sin (at)

A: Follow the procedure given below.

Q: For f(x) = In(sin(x)), find f'(x)? %3D

A: Given : f(x)=ln(sinx)

Q: Use the figure to write the expression csc y in algebraic form given y = arccos x, where 0 &lt; y…

A: By using Pythagorean theorem, we get…

Q: Find the tangent of LC. C 2/7 7/2 В Write your answer in simplified, rationalized form. Do not…

A: In a right angled traingle value of tan theta can be obtained by dividing the length of opposite…

Q: 3. Find if (a) y = 22" In (cot (7x)*) (b) y = sin? (Arcsin (T) +e-*)

A: Part(a) We have y=22xlncotπx2 We will use product rule and chain rule.  Product rule says:…

Q: What is the tangent ratio for zB? C B V5 A 1,

A: With respect to angle B, here, Altitude, a=2 Base, b=1 Hypotenuse, h=5

Q: Find the area inside the circle r = –3a sin 0 and outside the cardioid r = a(1 – sin 0), a > 0. -

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.