f(x) = -x² + ax + b, x < 2 (-ax + 7, x ≥ 2

Q: The degree of DE: (y")^2 +3y(y')+y^3 (y')^5 = 5x 02 01 05 0 3

A: Recall:  The degree of D.E. is the highest power of the highest order derivative in a D.E.

Q: Consider the following. Function Line f(x) = x³ 3x-y + 8 = 0 Find the slope of the given line. slope…

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Q: 2. Evaluate the integral. Do not use hyperbolic functions as the final answer. 1 =dx 2 √3x² - 4…

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Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: Q1: Find the for the following functions: dy dx 1- y = e(x+In 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh…

A: 1)y=ex+ln(5x) 2)y=cosh-1sin2x 3)y=xsinhx

Q: Evaluate the integral (1 + 2y)ªdy.

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Q: 5. Find the equation for the sphere whose center is at (-1, 1/12-13) and radius is

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Q: Suppose f'(2)=6 and g'(2) = 9. Find h' (2) where h(x) = 4f(x) + 3g(x) + 6. h'(2)=

A: Topic = Derivative

Q: 14) lim

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Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: Determine whether the series Σ n=1 convergent, or divergent (−1)” 7n-5 is absolutely convergent,…

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Q: i. Given that log x=12, log, y = 15 and log, z = 18. Consider the following four logarithmic…

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Q: Evaluate the following determinant by using row-operations. Carefully -1 3 4 -10 -4 A -> -4 -8 9 6…

A: To find the determinant of the given matrix A.

Q: Find the area of the region bounded by y²-x=0 and y²+x=2₁ A 2²—4² B (√2-1)u² C8u² 3 (D)

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Q: 3: Fill in the blanks in the following: 1 3. 4. If = (-12, 4, 8) the position vector of u…

A: Topic:-  vector algebra

Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

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Q: Evaluate fxsin zdz. 00 01

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Q: A tank in the shape of a right circular cone is full of water. If the height of the tank is 10 feet…

A: answer is in next step .please give a like !!!

Q: Find the general solution of the following 2nd order differential equation: y* +2y + 2y = 0

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: Topic = Derivative

Q: 1. Lim x-2 X x² - 4 x³ -x-6

A: Lets factor x3-x-6: x3-x-6=x3-2x2+2x2-4x+3x-6                =x2(x-2)+2x(x-2)+3(x-2)…

Q: How. Solve the diff. e que (4y-cosy) dy/dx=3x² = 0, y(0) = 6

A: (4y -cosy)dy/dx -3x2 = 0 y(0) = 0 here we do this using sepration variable method

Q: the appropriate integral to be used to find the volume of the solid generated? 8 7 6 5 4 3 2 1 -1 O…

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Q: Evaluate So * sin ada

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Q: ورد ه ی

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Q: For the given function f(x,y)=x²y³+3x³y, find a flay

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Q: 1 2. Lim x0x 1 sin x

A: Given:      limx→0+1x-1sinx simplifying we get     =limx→0+sinx-xxsinx Apply L'Hospital's Rule:…

Q: 6. y = x Arccsc (¹)

A: we can find the y' as below

Q: dy dx 11 1 + x-F y.x +5

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Q: A group of 10 individuals is used for a biological case study. The group contains 3 people with…

A: Concept of combination is used

Q: Write the equation of the line. == (0, 2) is on the line. Select one: O a. -3x + 5y = -10 O b. 5x -…

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Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: Question 15 The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the…

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Q: Find the radius of convergence, R, of the series. 00 (x-4)" n+1 n = 0 R = 1 Find the interval, I, of…

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Q: The partial fraction decomposition of f(x) g(x) + where 3 (x + 3) (x² - 4x + 4) f(x) = g(x) = -3x² -…

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Q: 9. Find the interval of convergence of the series n=1 5" (x-3)" √√n

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Q: 1. Find the area of the region bounded by y = x² - 3 and y = 5 - x².

A: This question can be solved using the concept of area bounded by two curves.

Q: Find the area bounded by the following functions/lines/curves: f(x) = 3x3 - x2 - 10x; g(x) = -x2 +…

A: Given: f(x) = 3x3 - x2 - 10x; g(x) = -x2 + 2x Let's first find the intersection point  3x3-x2-10x =…

Q: 1-x²dx 9-x²

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Q: y = 2 sin 3x 1+3 cos2x

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Q: If = (-12, 4, 8) the position vector of u is......

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Q: Solve the D.EXY+Y=1/1/2

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Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Can u do 6 and 7 . I will rate you thank you

A: step 2 complete solution

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

A: Basic identities of integration are used

Q: H.W : Prave the orthogonality. Conditions for the Sine and casine functions....

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Q: Question 3 If = 2/180°, A +C = −5 + 15j and C is the conjugate of B. Find A O 10-10j -10+10j O 3-4j…

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Q: Q4: If f(x,y) = x²y +exy Siny Find 1) 2) (D = f) at po(1,0) in the direction of 0 = Po

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Q: 7. Evaluate the volume generated by revolving the area bounded by the given curves using the hollow…

A: The given curves are x=4y-y2, y=x.   Now find the point of intersection between the curves…