1. lim Arcsinx-sinx y-0 (1-cos2x)sin2x 2-2cosx-xln(1+x) 2. lim X-0 xsin2x

Q: 1 (a) lim 2x+sin x 5x+2 (b) lim 1 (c) lim cos -

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: e implicit differentiation to find an equation of the tangent line to the devil's curve,defined by y…

A: Follow the procedure given below.

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Q: 2- i) By using L'Hopital Rule, find sinx lim x-0 e3x – 1 ii) Given that a = sin-1 , find ,csca

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Q: tinel the first, se cond-order derivative lf'cx) and find the slope at the given point xi: %3D

A: fx=1-1+x

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Q: 1-cos2 (x+y) 3. lim (xy)-(0,0) (r+y>)ety

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Q: B. Derivatives of Trigonometric Function Using the formula find- dx 5. y=cos (2x-1)

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Q: 3x²+x d (sin-()+sec='(x) (1) Compute lim cot-1(3x+*+1) (ii) Find- X+00 3x2-7 dx tan-1x+tan-1

A: i).…

Q: sin2x(1-сos2х) 7. lim X→0 (Arcsinx)-sinx

A: Given function is, Finding the limit, This is an indeterminant form. So, use the L'Hopital's rule.

Q: B. Derivatives of Trigonometric Functions dy Using the formula find dx 5. у-сos (2x-1)

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Q: a) Find the points at which the tangent line to the graph of function f(x) =x³ – 36x+60 has slope…

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Q: implicit differentiation to find y from dy dx 3. use 3•X 3..x• siny - Sy = = le

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Q: B. Derivatives of Trigonometric Functions Using the formula find- dy dx 7. y= sin In(4x + 3)

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Q: sec 2a cos ydy - (1 sin y) da = 0 %3D

A: Given:     sec(2x) cos2y dy-x(1-siny)dx=0 Re-arranging sec(2x) cos2y dy-x(1-siny)dx=0sec(2x) cos2y…

Q: Find the equation of the tangent plane to the graph of S(x, y) = In (4x² – y²) at the point (1, 1).…

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Q: Equation of the tangent of the curve y=sin(In x) at the apse x1 = 1 which of the following

A: Topic - equation of tangent line on curve First find the slope by differentiating The equation and…

Q: Find an equation of the tangent line to the graph of the function at the given point. You must write…

A: To find out the equation of Tangent line to the curve at the given point.

Q: sin3x d) lim x→0 + lim cos x + lim 2x² x→2 x-3

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Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: c. lim_sin x x- a. lim sin x %3D

A: We know that for any given functiony=fx, at x=a limit will exist if limx→a-fx=limx→a+fx

Q: lim a sin(1/2),

A: Given,           limx→0xsin1x

Q: B. Derivatives of Trigonometric Functions Using the formula find 6. y=tan Vx2 – 1

A: Let's find.

Q: الموضوع. 2/function, f- siniy -cesy bes- fix)= Sintx D Continu as At x= TTandEvenners I continnos At…

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Q: 2x - T find the equation Given the tangent funchions of y- 1-3+tan (") Of all its vertical…

A: y=1-3tan2x-π4 Now it can be written as, ⇒y=1-3·sin2x-π4cos2x-π4⇒y=cos2x-π4-3sin2x-π4cos2x-π4

Q: ldx on the graph y sec x? + y? = cos2x at point (1, 2).

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Q: sin x 1) lim- 2) If f (x)=x +1 then the equation of tangent at x-2 is y-4x-3. d 3) dx -2 2

A: find limit using L hospital Rule    Since you have posted a question with multiple sub-parts, we…

Q: 2y3 8. lim y-0 y-siny 9. lim(secx + tanx)csc X+0

A: To Find: 8. limy→02y3y-siny9. limx→0secx+tanxcscx

Q: a. lim sin x = c. lim_sin x = x-

A: We know that for any given functionfx at x=a, if limx→a-fx=limx→a+fx=b then limx→afx=b

Q: Exercise To Try 14 Find using implicit differentiation dx x² + 2xy – y +x = 2 (hyperbola) For an…

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Q: 4x 3-limx-0 tan5x sin(cos y) 4-lim, y- 2

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Q: ope of the curve 2xy = In(e*) sin(x)

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Q: Find the arc length function for the graph of f(x) = 3x2 using (0,0) as the starting point. What is…

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Q: curve of the tangent line to the c find theequatlo n -2X 3x + 1)° at xs0

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Q: Prove the limit statements

A: limx→0x2sin1x=0 Now since the range of sinx is -1, 1, therefore -1≤sin1x≤1⇒-x2≤x2sin1x≤x2 Now,…

Q: Q3/ lim Evaluate 2 (1+ cosx) ) sec x

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Q: Find the equation of the tangent line to the curve: sin-' (2x – y) – cos-(x – 2y) + = () at the…

A: Equation of tangent at point (x1,y1)  (y-y1)=dy/dx(x-x1)

Q: y = Arccot (cosx ) ; y' ' O sin x/ (1+ sin*2 (x) ) ) - sin x / (1+ sin^2 (x) ) ) sin x/ sqrt (1-…

A: Given y=cot-1cosx We will find y'that is the derivative of y. Chain Rule: If y=fgx, then y'=f'gx·g'x

Q: Find the slope of the tangent line to the path of a carnival ride x=7 cos(t)+ sin(7t), y=7 sin(t)+…

A: Here, the path is: x=7cos(t)+sin(7t), y=7sin(t)+cos(7t)

Q: 13. BONUS: Find the coordinates of all points on the graph of y=1-x at which the tangent line passes…

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Q: Arcsinx-sinx 1. lim y-0 (1-cos2x)sin2x

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Q: Find the x-coordinate of all points on the curve y = sin(2x) + 2 sin(x) at which the tangent line is…

A: Determine the derivative for y. y=sin2x+2sinxy'=ddxsin2x+2sinxy'=ddxsin2x+ddx2sinxy'=2cos2x+2cosx

Q: Find the arc length function for the graph of f(x) = 3x 3/2 using (0,0) as the starting point. What…

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Q: 3. f(x) = tan + 1 Period: 3 Positive Asymptote: Negative Asymptote: y-intercept: 1

A: Consider the function  f(x)=tan32x+1

Q: II sinx Find the slope of the tangent line to the graph of f(x)=: at x=- %3D cos x

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Q: 2x lim ¤→0 sin x

A: We have to find limit

Q: Find the values of h, k, and a that make the circle (x - h)2 + (y - k)2 = a2 tangent to the parabola…

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