Find the length of the curve. (Hint: u-s

Q: Solve the following differential equations of d²y_2dy + y = 2x dx² dx

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Q: Ex. (9) Solve 3y"-2y' + y = 4x+2

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Q: if any. Find the absolute extremum point(s) of f(x) = el-cost on [−5, π],

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Center (4, 6)

A: Given equation of circle is    x 2 +y 2 + 4x + 6y - 12 = 0   Now centre of circle is given by…

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

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Q: 21. 5₁ 1 dx (A) 2 So to dx dx both diverge when p = xP (B) 1 © DO dx and (E) -1 HOR LAY A DUPA

A: Divergent

Q: 5 13 And cos (a + B) 17) If sin α = and sin B = 12 13 π where a and ß are between 0 and " 2 evaluate…

A: We have to use simple trigonometric identities to solve the question

Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed |2x - 1| tan-¹(¹) 2x - 1 . lim…

A: LetL=limx→ 0-2x-1tan-11x2x-12x-1 is negative when x→ 0-.  Therefore 2x-1=-(2x-1)L=limx→…

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 3 P3(x) =

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: Let's find.

Q: IV. Do as indicated. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z.

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: Find the volume of the solid bounded above by f(x,y) = 8x², below by the xy-plane and the sides by y…

A: Volume

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 11x)y², y(0) - -…

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Q: Ex. (8) Sol Solve [D²-6D+9] y = 54x+18

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Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1

Q: Determine the interval of convergence for the series 2¹.¹. n=0 The series converges on the interval…

A: This is a geometric series with r=2x.

Q: Evaluate the definite integral 05/dx. Give an exact, completely simplified 0.5_6x² answer. Hint:…

A: Use  substitution method for solving integral.

Q: fe²x+Inx² sin x² dx = e2x cos x² dx

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Q: 31. (a) 32. (a) 33. (a) 34. (a) ₁12x-11dx • S²₁₂ √2+ |x|dx 2+ |x| L₁ let |e* - 1|dx *) ₁²³-1-15|dx +…

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Q: Describe the graph of the equation. r = (4 - 3t)i - 7tj O It is a plane in 2-space that goes through…

A: Given equationr=(4-3t)i-7tj

Q: d'y dx² d²y + dy dx X=

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Q: Replace the polar equation r. sin (0+ 1 (0+²) = 2 to Cartesian equation

A: See the details solution in below

Q: Find the average value of ƒ(x) = x² √√28 + x² on the interval [0,2]. favg= Report all answers…

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Q: V. Find the slope of the normal line to the graph of g(x) = where x = 0. log₂ (1-x) sin ¹(x) + e² at…

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Q: fx-²dx

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Q: Find A where R is the region R outside the circle and inside the V=2 Curve r= 4 Sing

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Q: Find the point on the curve y=x³ at which the tangent is parallel to the tangent at the point on the…

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Q: Use Squeeze Theorem to evaluate lim X→+∞ cos (x) log ₁/2 (x)

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Q: Describe the graph of the polar equation. 5r cos 0 + r sin 0 = 7 Line with slope 7 and y-intercept…

A: Explanation of the answer is as follows

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1 + ²/ 1. lim x12x² + x1

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Q: 8 sin 8. Then sketch the curve.

A: The correct curve of r = 8 -8sin(θ) is  Option (C)

Q: 1) fx-²dx 2) sin(n)dx

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Q: Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of…

A: Given problem:-

Q: Calculuate the length of the curvey = 4√2 3 3|2 within the interval of 0≤x≤ 1,

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Q: 2. y = tan-¹(cosh x) (sin² x) (sech x) secx [use logarithmic differentiation]

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Q: dy II. Find Do not simplify your answers. . dx 2. y= tan-¹(cosh.r) (sin²r) (sech r)secr [use…

A: Given y=tan-1( cosh x)( sin2 x ) (sech x)secx

Q: Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational…

A: Given: fx=36x2-12x+36x-3   As we know that; To calculate the vertical asymptote, equate the…

Q: 7. lim y→∞ y² – е6 y 4y² + e7y

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2x 3x lim x-2- (-²-2- -3X=42) x -…

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Q: Solve the following differential equations of d² y dx² dx dy +3 dv −10y=3x²

A: We have to find the solution of the given differential equation.

Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Range -8 ≤ y ≤ 2 -7 ≤ y ≤ 3 -2 ≤…

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Q: 5 If [F(x) dx f(x) dx = 7.4 and 1.°F(x) dx f(x) dx = 5.7, find [²1 f(x) dx.

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Q: II. Find dz Do not simplify your answers. 1. log,(√2x² + y) + tan(x − ³) = sin¹(x² - 1) +

A: We can solve this as follows:

Q: A factory operating at maximum capacity can produce 25 fuzzles in one day. The cost of producing a…

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Q: 27 If (2x 3) [133] [3] 3] -3 23 1. 2 13 2 2 3. 13 2 23 2 - 0, then the value of x is

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Q: ☎ Q1: If x=² and y=21³ then b) 3 314 ² dx d) at x=4 F others Choose

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Q: ● Let B(x) Let C(x) = = = **f(t)dt. Evaluate B(1). * f(t)dt. Evaluate C(9).

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Q: Consider the following. u = (-3, 3, 5) v = (0, 1, 6) Find u x v. Determine if u x v is orthogonal to…

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