5) Find the slope using y = (=/3² at 2 First Principle (-3,8)

Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

A:

Q: Evaluate 2 1 ² ₁² + √²³² - ²3/7 + 3x²³ - ²/3 d. X =)dx 3 X X 2 6.780 6.870 -6.870 -6.087 -0.687…

A: Given ∫12x3+x43-3x32+3x2-2xdx

Q: The value of the definite integral is Select one: O 16 3x²dx 0-8 O none of the others 08 0 0

A:

Q: Can you solve this? 10x8 5x4 A) 2x² B) 2x¹2 = ? C) 2x4 D) 2x32

A: Solve the given

Q: d²x x². - 5y = x + 1 is non-homogeneous second order differential equations with constant…

A:

Q: True or False: We have Select one: O True O False 0 8 √√xdx = 11.

A:

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

Q: Use the derivative f'(x) = x²(x - 5)(x + 5) to determine the local maxima and minima of f and the…

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Q: Evaluate the definite integral. 2 cot-¹(x) 1 + x² 1 - 1 dx

A:

Q: The derivative of a^u with respect to x is

A: Aim:- To calculate : ddx(au)

Q: Find r(t) for the given conditions. r'(t) = 8e4ti + 5etj, r(t) = (No Response) Need Help? Read It…

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Q: Calculate the area of the parametric surface given by: r(u, v) = 2 sin u cos vi + 2 sin u sin vj + 2…

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Q: In a pool filled with water to a depth of 1 Rectangular plate calculate the fluid force on one side…

A: Given: Depth of pool = 10ft Area of rectangular plate, A = 3ft×4ft=12 ft2  Hydrostatic Force on…

Q: At what point do the curves r₁(t) = (t, 5 − t, 35 + t²) and r₂(s) = (7 — s, s − 2, s²) intersect?…

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Q: Solve 2 sin² (t) + sin(t) - 1 = 0 for all solutions 0 < t < 2π t = Give your answers as a list…

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Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Calculate the mass of the sphere x² + y² + z² ≤ 4, the density at the point p(x,y,z) is proportional…

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x. (Give your…

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Q: Let a = (5, 5, - 3) and b = ( – 5, 3, 0). Find the projection of b onto a. proj¡ b = <

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Q: Consider the following. 2(x-8)² + (y - 6)² + (z − 5)² = 10, (9, 8, 7) (a) Find an equation of the…

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Q: an = arn+1 an = arn-1 * The general term of geometric progres Option 4 O anar" a" = arn-1 - Option

A:

Q: Differentiate the given series expansion of f term-by-term to obtain the corresponding series…

A: To find the derivative.

Q: Integrate (sinx + cos^2x)^3 dx

A: To evaluate: ∫sinx + cos2x3dx Let I = ∫sinx + cos2x3dx ⇒I =…

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0, 4, — 3), and R= (-6, -1, - 5)

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Q: Find all solutions to the equation. tan 0-1=0 Write your answer in radians in terms of it, and use…

A:

Q: For the following function f, find the antiderivative F that satisfies the given condition f(v) =…

A:

Q: 5. Find L¹ s-1 s³ -10s² +24s

A: To find L-1s-1s3-10s2+24s.

Q: =√₁²-1d₁ S²³ If f(x) = X u²-1 du then what is f'(3)? I

A:

Q: The general solution of the DE+4-5y=0 y= Ae* + Be5x Option 2 O y = Ae* + Be-5x y= Ae* + Be-5x Option…

A: We have to find the general solution.

Q: S cos 2x dx COSX

A:

Q: True or False: We have Select one: True False -8 √xdx = 64 3

A:

Q: ey+5 | ey-5 ولا

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Q: se series to evaluate the limit. 2 lim h→0 (sin h)/h- cos h h²

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Q: Find u-v, 2(u + 3v), and 2v-u. u-(6, 0, -5, 8), v= (0, 4, 8, 6) u-v (b) 2(u + 3v) - (c) 2v-u-

A: To find out u-v, 2(u+3v), 2v-u

Q: Find r'(t), r(t), and r'(to) for the given value of to. Then sketch the space curve represented by…

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Q: (a) (b) Evaluate S 9xsin (2-3x)XAMIMATION dx. *1*: FIDENTIA Evaluate 1 9x² +6x+ AL 123 CALCULU by…

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Q: Find the Maclaurin series of co E cos(x³). n=0

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Q: Solve: y'' - 4y' + 4y = 3e ^(2x) Show all work clearly please.

A: See the details solution in below

Q: Consider the following graph on the interval - 165° < x < 270°: 5 4 3 2 D 1 150-120 90 -60 -30 -1 -2…

A: We have given a graph of function and finding amplitude,period and function

Q: Find the line integral of the vector field F= over the curve C which is the quarter of the unit…

A: To evaluate the line integral of given vector field over the curve C.

Q: The function f(x) = 3x ln(1 + x) is represented as a power series f(x) = Σ cnan. n=0 Find the…

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Q: A particle in R2 has a velocity function of v(t) = (3t²-4, 6t + 2) (given in m/s). After moving for…

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Q: The distance from the point K(3, -2, 0) to the az- plane is Select one: O-2 O √13 O 0 02 O None of…

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Q: True or False: Suppose k is constant. Then 5 [² is equal to 10k. Select one: True O False kdx

A: Solve the given intregal

Q: 08 06 04- 02- }} ye y=0x=y² 02 yer* dxdy = 36 38

A: To switch the order of integration and then evaluate the value of integration.

Q: ³ [] (2² + y²) p(x, y, z)dV where p is the density function. Moment of inertia about z is calculated…

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Q: 100 100 suppose that Σ a; = -17 and Σ b; = 13. compute the sum. i=1 i=1 100 Σ ( – 30a; – 76;) i=1

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Q: Represent the plane curve by a vector-valued function y=1-x^2

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Q: Find the equation of tangent line for the curve f(x)=e³x at coordinate (0,1).

A: Given: fx=e3x