3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b) lim x0 sin² x () -12-21)

Q: 22. Find a domain for the quantifiers in 3x3y(xy^ Vz((z=x) v (z = y))) such that this statement is…

A:

Q: 1. The simple interest charged on a 60-day loan of Php 8,400.00 is Php 119. Find the simple interest…

A: Use simple interest formula

Q: A В D ľ КIN 5л 2 (2 — 4sin(0) + 2 sin²(0)) d0 (2 - 4 sin(0) + 2 sin²(0)) d0 (1 — 2 sin(0) + sin²(0))…

A:

Q: -X y" + 2y² + y = €²² ln x e^

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Q: Determine the general solution of y" - y = 0 given y₁(x) = e e-2x using reduction of order

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Q: = 10. Find a second-degree polynomial P such that P(1) = 7, P'(1) = 7, and P"(1) P(x) = Need Help?…

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Q: Find the area of the region bounded by the curves 1 y=; y = = 4 and the x-axis using vertical strip.…

A: Let's find area of the region bounded by curves and given line y=4.

Q: Evaluate each determinant.

A: A = -1523

Q: 3 f²f²² ²³ y cos(z³) dx dy dz 0

A: The given integral:∫01∫0z2∫03ycosz5dx dy dz

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Q: Evaluate the integral: ft² ns te" du ds dt

A: Let's evaluate given integral.

Q: 2-S Sin ³ x cos" x dx

A: SOLUTION-

Q: 3 Evaluate: (4x²yz - z dz dy dx 24

A: The integration of the triple integral is (4x2yz-z4/4), z from 0 to 1, y from -1 to 4, x from 2 to…

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A: Given function is differentiated.

Q: Solve the initial value problems dy 19. (x + 1)- dx -2(x² + x)y=x+1' x>-1, y(0) = 5 dy 17. 0 + y =…

A: Given (x+1)dydx-2(x2+x)y=ex2x+1       y(0)=5, x>-1To find Solution of Differential Equation:

Q: 6. Evaluate the line integral y²³ dr + ²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: In this question, we need to evaluate the given line integral.  The given vertices of rectangle are…

Q: an+1 Suppose that an ∞ Σ απ( – 81)" man n=1 →1 as n→ ∞o. Find the radius of convergence.

A:

Q: Find the number c that satisfies the conclusion of the Mean Value Theorem for this function f and…

A: This question can be solved using the concept of mean value theorem.

Q: Evaluate [x² √2x+1dx

A: Indefinite Integration

Q: 2. I. Evaluate each determinant. -4 3 -3 2

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Q: Find the general solutions for these differential equations: a. 2y²dx + (x²y - 2xy)dy = 0 b. y' =…

A: Use differential equation concept

Q: зи Evaluate the integral: So So So u s2 +u2 ds du dt

A: Given: I=∫02∫0t∫03uus2+u2dsdudt   As we know the common integral. ∫11+x2dx=tan-1x+C

Q: PARKING THIS BLOCK 2AM TO 5AM 2 HOUR PARKING THIS BLOCK 9AM 6PM EXCEPT SUNDAYS 15 MINUTE PARKING…

A: Ques (a) According to the third sign (at the bottom), the parking time is between 8 AM to 5 PM. So…

Q: Solve the general solution of the following linear differential equation: (y-cos²x) dx + cosxdy = 0

A: Given (y-cos2x)dx+cosxdy=0To find general solution:

Q: -2 Evaluate: ²₁5²[(x²-²²] | du dt x+y

A:

Q: Evaluate: du [(x²-y²)²1 ³₁ 1² du dt x+y

A: Given , ∫-13∫02x2-y22x+ydudt

Q: dy Write down a differential equation of the form dt 13 solutions all approach y = as t→∞. 14 y' = =…

A: The general form of the differential equation is  dydt=ay+b

Q: f(x, y) = = /25 - (x - 2)² - y²

A:

Q: Let f : R 7−→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find f^(−1)(x).

A: Let f:R→R be defined by f(x) = 2 - 5x.

Q: Evaluate the definite integral. 8 [x√x - 7 dx 5.06

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Q: Evaluate the integral by making the given substitution. (Remember to use absolute values where…

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Q: Evaluate the following * Sete e7x-³dx O e^(7x-3)/3 + C O e^(7x-3) + C - e^(7x-3)/7 + C O e^(7x-3)/7…

A: We will use substitution method to solve the integral

Q: 1. Find the Inverse Laplace Transforms of the following. 3s 2), 35544 2

A:

Q: Choose 1 answer: A 13 klo ㅠ 4t2 + 16 sec4 (t) dt

A: Please refer to the image below

Q: 5. Use Cartesian coordinates to evaluate ƒƒƒ v³² av where D is the tetrahedron in the first octant…

A: Given problem:-

Q: Evaluate: ³²₁₂[z³(x + y)³] dz dy dx

A: Given, ∫-43∫-12∫01z3x+y3dzdydx

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: (1) we have to fill in the blanks Let I be a proper ideal of the commutative ring r with identity.…

Q: True or False? 4. Let f : R → R be a function defined by f(x) = x^2+1. If B = {2, 5}, then…

A: according to the company rule we can answer only the first question and rust can be reposted.

Q: Solve the given differential equation. All solutions should be found. (5y¹ + 2x³y) dx − (4xy³ + x¹)…

A: Using integrating factor make equation exact

Q: For each of the following ,find fx fy fxx fy fyx and fxy f(x, y) = x cos+ ye*. 2.f(x,y) = y²x¹e². 3.…

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Q: 2 S Sec'x In cotx) dx (

A: We will solve the problem.

Q: 4 Verify that the Mean Value Theorem can be applied to the function f(x) = x 5 on the interval [0,…

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Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: 5. I. Evaluate each determinant. -2 -1 4 2 5

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Q: -3 -t Evaluate the integral: Soft²eu du dt е

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Q: Let F(x,y)=ln(x² + y²), then answer the following (4) Find the boundary of the function's domain.…

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Q: Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y²-3x2 and the…

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Q: Consider the parametric curve: X = = 7et y = 3t5 Which integral gives the arc length of the curve…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: (5) If f(x) =........, then f(x) is reducible in Z5 [x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x²…

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Q: classify the following PDES :- 827 827 дхг 82z =X+Зу +2 буду дуг 2 2 X ох Иxx - 2xy Иху +Ў Иуу X •…

A: