Lim (ره) (x,y) Sin (x²+ y²) x4yo

Q: T² 2 / (x + 1) (2² + 1) dr. Evaluate

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Q: arcsin(4x)/arctan(5x)...

A: Using L'Hospital's rule to evaluate this limit,we know that,if  is of the intermediate form or…

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: lim Sin (x-B) XB (x-B)

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Q: sec2 () dx x3

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Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: Let fx) = x + 2x and g(x) = x- 5. a) Find (f ° g)(x). f(x+h) – f(x) b) Find the difference quotient…

A: Given

Q: -4e sin(7y) 4e sin(7y) ду

A:

Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: sin ( C + D ) =-------------------

A: Our Aim is to tell Sin (C+D)=?

Q: x° + x2 + 1 (c) dx. x3 – x2 +2x - 2 arctan x (d) x2

A:

Q: e* tan (e*) dx sec2 (e*) – 7

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: cos x tan x a) lim x→0 2x (x2 b) lim sin(x-) 4 x- 4

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Q: Finf the equation of the tangent line to (cos(x)ex10x)/(Sec2(5x)+1)+11 at the point (0,11)

A: Given,           The equation of the tangent line to (cos(x)ex10x)(sec2(5x)+1)+11  at the point…

Q: f(csca cot a + ba*)da csc * +x6 +e cot & + x + e 6 CSC * - +c CSC * +z6 - csc * +a +e .6 CSC * – *°…

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Q: Evaluate: 3 A 1–x*) 2 + C 3 (1-x*) ² + C --(1-x*) ² +C D 1-x*) 2 + C 3

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Q: Prove that a b π √√(x − a) (b − x)dx : = (b-a)² 8

A: To prove that,  ∫abx-ab-x dx=π8b-a2

Q: Sx [x²cox dx U. V x² Sax - S(α (x²) [ cond) dx dx x² (sinx) - -S 2x Sinx dx U. V. x² sinx - [2x…

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Q: Lim メートo Cos aX Cos bX

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Q: Y(6) = cot(5s)- 3 tan s - csc (5s)- 3 sec' s s:y (s) |

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Q: sin3 x dx (③)글 4 () (0)

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Q: Calculate facos xdx . (a) rsinr – casz+c (b) Icosz+sin x+c (c) zcost-sin x+c (d) Isinz+cOSI+C (e)…

A: Formula for integral by parts :        ∫u(x).v(x) dx=ux∫vxdx - u'x∫∫vxdxdx+…

Q: ● ftan(x) sec(x) dx

A: We will use substitute method to solve the integration

Q: cot(sec(x) -1 cot\sec

A: on  simplifying we get

Q: y? lim (х.у)-(1,0) х2 + у? — 2х + 1

A:

Q: lim (x, y) - (6, -2) (x?y + 5xy2 + 4)

A: NOTE: Refresh your page if you can't see any equations. . substitute x=6 and y=-2

Q: (x² + 1)ª (2.x + 1)3(3x – 1)5 y =

A: Simple differentiation problem....

Q: d dx x= ||

A: Given that

Q: Q3) a) find f sec³ x dx

A:

Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

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Q: Distance between (9x,-11x)and(4x,x)

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Q: Ssec? [sec(4x)tan(4x) dx (p sec (5x +3) dx e) f sin 3x + 1. dx 2x +4 f)

A: We will solve the following

Q: -1 sedx- cos(

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Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

A:

Q: Find sec2 (2x) 1- S (tan2x-4)9

A: Since multiple questions are asked, according to guidelines I am solving the first question. Please…

Q: (d) v1+ tan x =1+;x

A: To prove that the following approximation holds, 1+tanx≅1+12x