Question 4. Prove that L°[0, 1] C L°[0, 1). Hint: Hölder's inequality

Q: Question 11 puas √1+1² Ffxx)=f -dt, then f'(x) equals 0 I+e' In(secx)√1+tan²x Itela tanx sec³x 1+ele…

A: Topic:- application of integration  Note :- as per our guideline if more than one question uploaded…

Q: Question 7 2²e"² sin(x²yz) Let f(x, y, z) 12 find dyəzə"x at the point (3, 0,0) 4 8.

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Q: Question 18 If f(x) = fr30cos(t)dt, then f'(VT) = 37 sin (7) cos (n) B. C 37 COST Зт сos (т)

A: Find the derivative of f(x) using  fundamental theorem of calculus

Q: Question 1 If z=lm/x*+ y² + un /x²+y²+-tan 12 then the numerical value of dy? dx2 is equal to...-

A: Given- z=lnx2+y2+12tan-1yx To find- Numerical value of ∂2z∂y2+∂2z∂x2 Here we will use the following…

Q: Question 10 Given z = (e-22) (sin y), find 92 O-2e-2 O-2 e 2 (sin y) + e-2 (cos y) O-2e-2 (sin y) -2…

A: We have to find derivative of given term.

Q: Question 8 Given f (x, y, z) = zey - x sin-¹(3), what is fzz |ƒ(0,2,1)? 2e² 1 1 √√3 1 √3 none of the…

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Q: [et Suppose A(t) =0 0. cos t sin t, show that A(t)-1 exists and then find it. - sin t Co t. -

A: Given- At = et000cos tsin t0-sin tcos t To Show- Show that At-1 exists and then find it.

Q: Question 1 Which of the following sets of functions are linearly independent on (0, ∞)? O {1, tan²…

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Q: Question 4 When x°cos (x²)dx is evaluated using IBP, the value of J v du is? A B -cos (x2) cos (x2)…

A: We need to choose correct option.

Q: QUESTION 2 27 元 +icos 9. TC sin 9 1-i 0-i 0 +i 1+ i Windowsi

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Q: 1-S Ca-メ)xde

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Q: Question 18 Solve the equation on the interval 0 s 0 < 2n. 2 sin? 0 = 3(cos 0 + 1) o f

A: Consider the given equation, 2sin2θ=3cosθ+1 Convert the equation cosine form.…

Q: Of the following, which are acceptable wavefunctions in the range x = -infinity to infinity and…

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Q: Question 8 D I cos(2z)dr = %3D A sin(2z) +C B cos(2z) + sin(27) +C c z sin(2z) – ocos(2r) + C 글프…

A: Basics of Calculus.

Q: Kreyszig Chapter 1, Section 1.5, Additional Question 01 Find the particular solution for the given…

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Q: Question 6 Evaluate using Wallis Formula: cos 2x dx 3 16 3 16 8. 32

A: Topic - definite integration

Q: set E: Problem #6 Find the equation oF the line tangent to at x = 5r FCx) = cos?x -sin? ) %3D

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Q: Question 19 Given f(x,y) = ex cos y, Evaluate fx(0,2) A) e² B 0 (C) -sin 2 D) cos 2

A: Topic = Derivative

Q: Question 1.i.) A truncated sine wave { sin5x, -T <x <T y = f(x) = 0, otherwise

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Q: Question 4 cosh (T-i) = e cosl - i e sin 1 + e cos 1 + ie sin 1 e cosl + i e sin 1 e-I cos 1 + i e…

A: Simplify the expression: coshπ-i

Q: Question 1 Differentiate: arcsin Oy/x 01 O x/y O (E) None of these 0 0 (# )+ + arccos (²-) = 1

A: Differentiation

Q: Question 1. Find the general solution of the following ODE: y" – 4y' + 3y = -6e² + 40 sin z.

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Q: Problem 3. Prove that 2 (b) L(r} : a (a) L{sin at} : %3D s2 +a? (c) L{cosh at} : 52 – a²° -

A: Explanation of the solution is given below...

Q: Question 3 Differentiate 5* sec(e*) (A 5* sec (e*) [e*tan (e") – In 5] B 5X In 5 sec (e) [tan (e) +…

A: we have to differentiating  AS per guideline we have to solve one question

Q: 20 cos COs 47. lim e e>0

A: By using the formula cosx+cosy=-2sin[(x+y)/2]sin[(x-y)/2], we have

Q: Question 1: Let y(r, t) = x'tº + 2x – 3t (a) What is du/az? (b) What is du/a?

A: We have , yx , t = x7 t9 + 2x - 3t We need to find , ∂y∂x and ∂y∂t. We know that , partial…

Q: Question 6 S sin(x) dx = a) sin ()x + C O b) - cos(x) + C O9 - cos(x)x+ C Od) x+ C

A: Given query is to find the integral of sin(π).

Q: 3. K. 16 • sin L = sin M = 34 • cos L = • cos M = %3D • tan L = • tan M = %3D M O Gina Wison (All…

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Q: Kreyszig Chapter 1, Section 1.5, Additional Question 01 Find the particular solution for the given…

A: Given equation is: y'+25*ycot5x=30cos5xyπ10=4 Simplifying the differential equation: The integrating…

Q: Question 8 A Ísec xdx= tan z + C A B) csc?z + C cosz +C

A: AB8 Q.8) The given integral is ∫sec2xdx

Q: Problem 2 Let { sin(x-y) f(r, y) = |피 + 1yl # 0 (x, y) = (0,0) %3D %3D Is f continues at the origin?…

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Q: B 3 Not drawn to scale 3 ,cos A 5 3 ,cos A 4 sin A sin A c. a. 3 5 4 , cos A 5 3 cos A = 5 sin A b.…

A: It is known that in a right angled triangle,

Q: IN QUESTION 18, FIND THE EXACT VALUE OF s IN THE GIVEN INTERVAL THAT HAS THE GIVEN CIRCULAR FUNCTION…

A: topic - inverse trigonometric functions

Q: Question 4 of 10 m(x) = sec²(e2r+1) %3D Select the correct response. 20+1 sec(e2r+1) tan(e2r+1)…

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Q: Question 14 Find d-Y/dx? at the given point without eliminating the parameter. *=0+cos® and y= 1+…

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Q: set D: Problem #G Find the eauation OF the Iine tangent to F Cx) = cos? x - Sin? (x) at X 3r %3D 4

A: To find the equation of the tangent line at x=3pi/4.

Q: QUESTION 16 Which one of the following points lies on the curve r= sin 0 – 5. o (-5, n) (-s. =) 2…

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Q: Question 4 (The Fundamental Theorem of Calculus). if y = sin (t- 1) dt. dy Find if y = dr cos? x O -…

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Q: Question 1.i.) A truncated sine wave { sin5x, y = f(x) = 0, %3D otherwise

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Q: QUESTION 14 Which one of the following points lies on the curver = sin 0 – 5. o(-5, n) -5, T1) o (5,…

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Q: Problem 1. What is the distance travelled by a point during the time t, if it moves in X- Y plane…

A: Given that x=asinωt and y=a(1-cosωt) are relative to each other. We need to find the distance…

Q: QUESTION 18 2ay" = 17 when =/2. y' "x= Arctant3, y=V1+r6, find the value of a if O -22

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Q: Question 10 tanx If f(x)= A (B) C D sec ³x Itelin sec²x Iteline 1+1² I+e' -dt, then f'(x) equals…

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Q: Problem 2. (a) Simplify the expression cos(arctan x), x > 0.

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Q: 4 T <a < m; cos ß = .0 < B <% =5.0 <B < 37. tan a = %3D 3' 2

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Question 13 The integral csc(0.5) dx is equal to A None of the given choices B2ln|csc(0.5x) +…

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Q: ди Ans, u = e"(A,er" cosh ax + Bjehar" sinh ax) e ka't cos ax + B,e¯ha" sin ax) -ka’t, u = e"(A;x +…

A: Given PDE is k∂2u∂x2-u=∂u∂t,  k&gt;0          (1) Let the solution be u=XT, where X and T are the…

Q: a(t) = sech () tanh ()-ež. I t cle.

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Q: Question 1 Write acceleratin a in the form of a = arT +aNN without finding T and N. (a) r(t) =…

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