Euler's diFFQ 3. Eqc) ((x) -24(x)=x(y しx1) ucx1-2uしx1 = x 1u(x) )

Q: i) Find the tangent and normal lines to the curve r*y° +sin(xy)+ln(1+y)+sin(2x) = sin(2) at the…

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Q: B) Derivative following functions by using chain rule method 1) y = 5u³- u? , 2x = 4u? 2) у %3D |1 ,…

A: Answer (1): Given that, y=5u3-u2, 2x=4u2 Suppose fgx Then, to find the derivative apply the chain…

Q: Ý ху X Sin

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Q: 4) lim 2Sinx – /3 = ? 2л - 3х 3

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Q: 11) Find the derivative of y = 3x (2æ² + 5x) Use two methods: Product Rule and Foil First method

A: Find the derivative of y

Q: 16. etan (1) sec² (x) dr

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Q: The basic idea of optimization is that we have a quantity (represented by a function), and we need…

A: The basic idea of optimization is to find the maximum or minimum of a function using the different…

Q: Find the first and second derivative of (x^3-3x^2+5)/(x^3+1). I found the first derivative, I…

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Q: arcsin = ab x² – Va² – y²; Find y'.

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Q: rin 2 e2# sec-"(e")dr

A: Solution

Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

Q: 1) lim y-4 x+6x+5 2) lim 2-3x-4 t+3t2-12t+4 sin3h-2h 3) lim 4) lim 3-4 gin

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Q: sin 8 What is the exact value of Show your work for partial credit.

A: Find the value of sin(7pi/8).

Q: ifferentiate the function: y=(x^4 sin^2(x))^(3)

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Q: 3. U sin g Derivative Product rule 3. (x + 6) (x + 5); 4. 4x² (x – 1)

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Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

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Q: How to solve linear Diophanfine equation

A: See the attachment

Q: compute the derivate

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Q: sin xV1+ cos 2xdx 6. V1 - sin 2xdx 7. 8. cos' xdx 1+x+x? -dx x² + x3 9. I sin 2x 10. I + sin² x xp-

A: Note: As per company policy we are supposed to solve only one question, So kindly repost the other…

Q: Evaluale tim xin xs

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Q: solve parameter method J-yこ cosh x y"-

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Q: e3x _e-3x Y = e3x +e-3x]

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Q: Find y" by implicit differentiation. 2x3 + 3у3 3 2 -4x y" = 3y2 Need Help? Read It Watch It

A: We have to solve the derivative

Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: sc 2x - cot 2x = 0 1 sec²x

A: We can find the answer as below.

Q: 2) y - • sin 0 +2 3元 2元 5元 3元 元 元2

A: The given function,       y=12.sin θ+2

Q: 2y-n у-п lim п cos y y-

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Q: 7. y = 4 e2x, 4th derivative 8. y = -5 e3x^2, 2nd derivative 9. y = 7 In 7x, 2nd derivative

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Q: antiderivate of y = sin x + 6x2

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Q: Derivatives of y = 3x²(x² + 1)³

A: We can find the derivative as below.

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

Q: Numerically integrate f (x) = x³ + 3x? + 4x = 2 using Single-Trapezoidal Rule. 6 from a = 1 and b -…

A: (1) solution

Q: =x+6 Line 1: y= 2 Line 2: y=x-1 =-x LI

A: In system A, L1:y=x+6L2:y=-x The graph of the lines are intersect at one point. Hence there is…

Q: sinh-1x = In (x + vx² + 1) %3D

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Q: 5 - x2 + 2x – 3 = 0

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Q: Lim -> 0 Sin3ycot5y/ycot4y

A: limy→0       sin 3y .cot 5yycot4y   =limy→0    sin3y tan4yy tan5y 00farm…

Q: On the interval -2<x<-1/2, the graph of the curve f (x) = 2x° +3x2 - 12x - 7 is: %3D Support answer…

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Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: )etan²x f'(x) = (tan² x)et %3D Option 2 g tan?x f'(x) = (2 tan x)e

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Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

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Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: 1. Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at…

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Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…

Q: separable 9-X(2lnX+1) Sin y+ ycosy

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Q: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

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Q: 3 8. y = sec Зx) 9sec (2 – 3x)tan´(2 – 3x) B. - 9sec (2 - 3x) tan tan (2 3 С. 9 sec' (2 — 3х) tan…

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Q: 5-7 -1 Using quotient rule, show-that d [cotx] dx 2. 1+x

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Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step