1. r(t) = ti + (In cos t)j, -T/2 < t < T/2

Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

Q: ³ sin y - 3) = √10 ² Let f(x, y) dt 1 + cos² (t) 16 Then f (2, π/6)=

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Q: S Q16) L−¹ {(8 − 1)² + 4) (A) et [cost + sin t] (D) et [cos 2t+sin 2t] (B) et [cos 2t + sin 2t] (E)…

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Q: Which of the following equations is FALSE? * O tan t = tan (t + 2m) where t n/2 + kTI O tan 2t = tan…

A: tant+2π=tant+tan2π1-tant·tan2π    ∵tanx+y=tanx+tany1-tanx tany=tant+01-tant·0=tant Therefore…

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: Let A be the set of irrational numbers in [0, 1] and let B be the set of ratinal numbers in [0, 1].…

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Q: -1 What is the range of the function y = cos ( +1)? 이[-2,이 O [0, T| T o (0, 7)

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

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Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

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Q: Let a(t), 2 < t< 8 be a positive function. Also, let the function 8(t) be defined as a'(t)/a(t) on…

A: We will find out the required expression.

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

Q: . What is F(/3) if C = 0?

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Q: Prove or disprove: For n > 2, n − 1 is a generator of U(n)

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Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: 07/ Express in the form x + jy (1) e'(x/2-j) (2) In(3 – j) (3) sin(r/4+ j2) -

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Q: ||r′(t) × r"(t)|| ||r'(t)||³ r(t) = 4 cos(t)i + 4 sin(t)j + tk Use the formula ñ(t) = to find (t).

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

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Q: Q11\ Express in the form x + jy (1) e(z/2-j) (2) In(3 – j) (3) sin(t/4+j2)

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Q: What is the range of f(x)-¹ = cos¯¹(0)₂ A C D [-] 2 2 [0, π] [-1,1] (-∞, ∞0)

A: Given query is to find the range of the function.