Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

Q: 13. The range of the arcsin or sin(x) is: a) (0, 2.7) b)(0, 7 ) ) 0. d) 4 '4 e) 2'2 4

A: 13) Given

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A: Using the chain rule of differentiation,

Q: 18. Use periodicity to express sec in p given that sin

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Q: H.co/prove That;- CoS z

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Q: cos(: sin@)]=[- sin(esin@)]. * (b) (i) Show that - cose dt

A: We will use product rule of differentiation here

Q: -5 sinx dx I = =? ecosx +3e-cosx ) +c COSX a) arctan 3 cosx b) arctan + C

A: To find ∫-5sinxecosx+3e-cosxdx

Q: 2 sec wdw a) 1

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Q: 11) fx-In x dx In x- 2 4 (ans. : -+c) 12) fx- tan'x dx (ans. : 2 -tan"l x -(x- tan"" x)+c) 2 13) fx'…

A: 11.Given,∫x.In x dx

Q: 0 00 Co o o o sin (²) = √³ انه ده

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Q: Lan: prove (:) - - 4. sin x tan =1- cos x

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Q: The function y = 2x – cos x have two variables (x and y), these variables called

A: Here, the given equation is y=2x-cosx , which is a function of two variables(x and y). The name of…

Q: Let fx) e sinx. Calculate and simplify f "(r)

A: Compute the second derivative for the given f ( x ).

Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: Given f (t) = t^2 and g ( t) = sin 2t, obtain the convolution (f * g). -ea* -1- cos21) -er -1- cos…

A: Convolution Theorem : f * g t = ∫0tf(u) g(t-u) du   Integration by parts : ∫uv dx = u∫v dx -…

Q: tan u = dx du sec?u · dx

A: To prove: d(tan u)/dx = sec2u (du/dx)

Q: - IF z = tan2 -1 y Show that x- ây

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Q: FIHD THE DERIVATIVE OF THE GIVEM. FUMCTION Cos? x 1-) g(x) = 2)f(x)= Sinメ tany Sinx tan y sec x Cot…

A: topic - derivatives

Q: Differentiate: y = cos(5 e* ) e11 COS

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Q: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

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Q: < sin!!), w5"1)? aiong.seni-circle. 4) Work done by o trom tJ5, 1) to' (-3,-1) t radius 2 · 个。 3+1…

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Q: Find the edlution of the following equstions: (osx<r) a) cosx- casx =0 . b) tan2x = 3 tan X Sin8X .…

A: We have to solve the following equations.

Q: 4. The 1" derivative of y : cotx a) xsec?x + tanx b) xsecx - tanx c) cot x + xcsc'x d) cot x - xcscx

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Q: Suppose f (x) =cos(4- ). Evaluate: A - 3sin x- B D 3sin

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Q: Let f(x) = (8 sin z + 2 cos z)tan f'(z) -

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Q: d-) sin x cos??x dx =) 2. d-) Sin`x cos

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Q: 4. (a) cos=- -5/3 and sin >0, tan = 5 11 (b) (c) √11 5 (d) √11 6

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Q: 10 8- A 6- 2 -10-86 246 8 10 B -8 MathBits.com -10

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Q: If, Sec t-1/sec t +1 = A-cos t/A+cos t Then A =

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Q: fcos:fin x - sin' x )dr.

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Q: Suppose f(x) =sinx-4). Evaluate: | = )dx A - 3cos (D 3cos

A: Given; f(x) = sin(x/3 -4)

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A: Given,           12-32ix+yi=cosπ3+isinπ3-5

Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

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Q: What is the period of the function y = 10 sin(( - )) + 25? Х 4π 3 3π 4 O 3 4 حرام

A: Given thatIf a wave function is given as then period will be