2. Let f(t) be a continuous function on the interval [0, 27]. Suppose the 1st order Fourier approximation to f(t) is 1 – cos(t). Prove that " f(t)²dt > 3n.

Q: Find the linearization L(x) of the function at a. 9 f(x) = a = 3 - L(x) =

A: We have to find the linearization L(x) of the function at a.  We have, f(x)=9x and a = 3 

Q: Let f(z) = z – 6z. Calculate the difference quotient (3+h)-{(3) - for h = .1 h = .01 h = -.01 h = -1...

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Q: A. ā xb = b x ā B. Jā + 5| = |a + b| C. It is possible for la + b| < [ā|

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Q: proj„b is always less than |5 1|

A: We will use the definition of projection vector and will use the Cauchy-Schwarz inequality.

Q: The plane containing the three points (2, –1, –1), (2, 1, 8) and (1, 0, 6). Please write th

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Q: Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder. ...

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Q: Find of the fo lloming function the derivative Tin C A y'= (Sinsc) oc Sin 6-1 Sinac +Inx cos scl + I...

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Q: lā + b| = |a + b|

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Q: f(x) – f(a) Simplify the difference quotient for the given function. X-a f(x) = 4 – 2x – x?

A: Given query is to perform indicated operation on the function.

Q: Evalvate the limit lim Cos x In(x- TT Xーつク nピ-e)

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Q: 6 and its graph, use the graph to determine the following. r(x) 10 하 6 4 2 -4 -3 -2 -1 -2 1 2 3 4 -8...

A: where f'(x) is positive f(x) will increase and f'(x) is negative then f will decrease , observe the ...

Q: Find the derivative of the function by the limit process. Find an equation of the tangent line to th...

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Q: Consider the following function. x2 + 2x + 2 2 x3 3 (a) Find y' = f '(x). f'(x) = (b) Find the criti...

A: Given: - The function is, y=x33+x22-2x+2 To find: - (a) The derivative of the given function. (b) Th...

Q: Critique the validity of the expression d2y dy dx2 dx A) It is not valid, because the notation d?y d...

A: The objective is to critique the validity of the expression. 

Q: A trough is 16 ft long and its ends have the shape of isosceles triangles that are 3 ft across at th...

A: A trough is 16 ft long and its ends have the shape of isosceles triangles that are 3 ft across at th...

Q: Find the Taylor series generated by f at x= a. f(x) = 2*, a = 1 Choose the correct answer below. O A...

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Q: The population of Hungary has been modeled by P = 9.919(0.998)',

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Q: Evaluate the lim lim

A: We will find the limits. 

Q: For the following functions. Please show all evidence. (a) Identify all local extrema, (max or min.)...

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Q: If f(x)=x, then f'(5) = (A) 0 (B) 5 (C) 1 25 (E) (D) 5

A: Topic:- derivatives   

Q: Find the indefinite integral in each of the following. Show all necessary solutions. 3. sin ? x cos'...

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Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series c...

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Q: 1+x2+y2 Determine the set of points at which the function F(x, y) = is continuous. 1-x2-y2

A: In this we have to check Discontinuity of equation. 

Q: Find the tangent line to y = x -x+7 at x = 7. ,2 The tangent line to y = Vx -x + 7 at x = 7 is y =

A: We have to find tangent line

Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), и %3D (5,2,...

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Q: 3 cos(cos-1() 10-

A: SOLUTION-

Q: Calculate the improper integral if it converges, or show that it diverges. 1 dx -

A:

Q: [sin (21x) dx

A: ∫sin4(21x)dx Note- sin2x=1-cos(2x)2 and cos2x=1+cos(2x)2

Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),...

A: We have to find dsdtt0=π4

Q: Perform the following operation with the vectors а3(2. о, з>. ь-(з. 1, 2) %D |2a– 3b|

A: Given that: a=&lt;2, 0, 3&gt; and b=&lt;3, 1, 2&gt;

Q: 00 Does the seriesE(- 1)"n³ converge absolutely, converge conditionally, or diverge? n= 1 ... Choose...

A: Given series is  ∑n=1∞ -1nn323n To determine whether the series converges absolutely, converges cond...

Q: If f(z) = 2z2 + 6z + 3, find f'(-1), using the definition of derivative. f'(-1) is the limit as z of...

A: We have to find limit and tangent line

Q: Given the graph of f, find any values of x at which f'is not defined. 1 -2

A: Graph of the function is given, we have to find the values of x for which f'(x) is undefined

Q: 1. Identify the degree, end behavior and roots (with multiplicities) of the following polynomials. (...

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Q: Find the value of (f o g)' at the given value. f(u) = u° + 9, u= g(x) = Vx, x=1 (fo g)'(1) = (Type a...

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Q: Any line perpendicular to r(t) = t+ ·

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Q: • If we did not have logarithmic differentiation, what rules would we need to use to find the deriva...

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Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = e*Y sin(y)

A: The given function is: fx,y=exy siny To verify that the conclusion of Clairaut's theorem hold for th...

Q: Find the equations of the items described below 1. Any line perpendicular to r(t) =t+ 2. The plane ...

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Q: Given the side length b = 9 and the angle B = 43° on the triangle below, find the lengths of a and c...

A: Given that:                              

Q: 2. Let E be the piece of the cone z = Va² + y² lying between z = 0 and z = 1, oriented with the 'out...

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Q: Entered Answer Preview Result 23 23 correct -3 -0.0241935 incorrect 124 At least one of the answers ...

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Q: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

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Q: Determine whether each integral is convergent or divergent. Evaluate those that are converg 1 9. d.x...

A: If limit of improper integral is given and is finite, Then it will converge.

Q: Given y = f(u) and u = g(x), find dx = f'(g(x))g'(x) for the following functions- y = sin u, u = 4x ...

A: Please see the solution given in step 2

Q: S(x) 2 -1 2 3

A: The objective is to find f(-4).

Q: Find the point (x,y), at which the graph of y = 6x + 6x - 5 has a horizontal tangent. 2 The function...

A: Topic = Derivative

Q: 3. Evaluate all the first partial derivatives of the given functions at the given point. of of 1 a) ...

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Q: Compute the surface area of a surface generated by revolving the curve c(1) = (6 sin²(1), 6 cos² (1)...

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Q: Compute the partial sums S2, S4, and S6. + 1.2 5 + 3. 4 + 2.3 S : S4 = II

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