1. Determine the type and stability of the critical points of the homogeneous systems: (b) 4 = x + y – 7 = 3x – y - 5 dt

Q: Find the partial derivative of the function g(r,0) = r cos 0 + r sin 0.

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Q: 9 Select the conic section represented by the equation. 4y - 3 = 0 parabola line ellipse…

A: We will find the conic section which is represented by the equation.

Q: Express the repeating decimal as the ratio of two integers. 0.3 = 0.3333. The ratio of two integers…

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx +5 at x-2? %3!

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Q: Find the curvature of the curve defined by F(t) = e"i + 4tj K = Evaluate the curvature at the point…

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Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: Find the exact length of the polar curve described by: r = 9e-0 5 on the interval -T <O<67. 6

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Q: Verify Green's Theorem by evaluating both integrals ax dA ду for the given path. C: rectangle with…

A: From: (0, 0) to (5, 0)y=0, dy=0∫ y2 dx+ x2 dy =0From: (5,0) to (5, 9)x=5, dx=0∫09 x2 dy= ∫0925…

Q: Find the area of the shaded region Blank 1 Note: Enter exact answer x = y 20 1000 y? 20 ||

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Q: 3. The possition function s(t) = -1612 + 30t %3D Find : (a) average velocity over the time int erval…

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Q: Evaluate the sum: 2k), for n=21. k = 1

A: We can find the answer as below.

Q: 10) Calculate a lower sum for f(x) = 2x + 5 over the interval [0, 2] using 4 rectangles. %3D

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Q: Find the interest and amount due on a loan of Php 54,000 at 15.6% per year for 100 days.

A: Find the interest and amount due on a loan of Php 54,000 at 15.6% per year for 100 days.

Q: Q2) Find the integral value for the following functions 3x 1. S V1+3x2 dx 2. S(sec(4x) – 1)? dx dx…

A: LetI=∫3x1+3x2dxTake the constant out:  ∫a·fxdx=a·∫fxI=3·∫x1+3x2dxPut…

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x0 sin 2x x2-16 2. lim r14 (Yx+5)-3

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Q: Write out the first four terms of the series to show how the series starts. Then find the sum of the…

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Q: please answer quickly

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Q: dx 4. S

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Use the Quotient Rule to calculate the derivative for the function w(x) = at x = 4. Vx+x (Use…

A: Given the query is to find the derivative of the expression.

Q: Suppose that z = x/y, where x and y are differentiable functions of u and v such that x = dx/dv 3, у…

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Q: D(X) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

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Q: A rectangular picnic area of 8000 m² is being constructed along the edge of a river. It will be…

A: Explanation of the answer is as follows

Q: The line of intersection of the planes 2x +y - z= 4 and 4x – y+3z = 2 has equation %3D O a) (x, y,…

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Q: A football is kicked from the ground 70 yards along a parabolic path. The maximum height of the ball…

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Q: The directional derivative of the function f(x, y, z) = x²y° – 2z° at the point (1, 1, 1) in the…

A: We want to find directional derivative in the direction of the vector

Q: Use properties of logarithms with the given approximations to evaluate the expression. log 3x0.477…

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Q: An oil tank is being drained for cleaning. After t minutes there are Vlitres of oil left in the…

A: This is application of derivative problem

Q: t or points for each ase portrait on this page. dx = 2x – 2y – 4 and- = x+ 4y +3 dt dt GURE 6.1.

A: Given

Q: Determine the conjugate radical of the expression -8+35. O-8 -35 O NE + 35

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Q: Consider the function f (x) = - 3x³/% Which one of the following is true? O a) f is decreasing when…

A: If f'(x) &gt; 0 for all x in an interval I, then f(x) is increasing over I. If f'(x) &lt; 0 for all…

Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

A: Since there are multiple question the first question is answered as per our guidelines. Kindly…

Q: Write the general conic form equation for an ellipse with center at (-1, -1), vertex at (5, -1), and…

A: This question can be solved using the concept of general equation of ellipse.

Q: Use logarithmic differentiation to find dy/dx. 4 y = x> 2 x* + 4 dy dx

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at x-2? %3D

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Q: Q2) Find the integral value for the following functions dx 4. S x2Vx2-1 ecos-1x 5. S dx V1-x2 6. Se…

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Q: On each interval, determine whether the graph of f(x) is concave up or concave down. From x=1 to…

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Q: dx 4. S; x2Vx2-1

A: Given: I=∫dxx2x2-1   ...1 As we know that; The trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: Q3) A) If you have three functions: f(x) = x2 – x %3D | g(x) = 3x – 1 w(x) = x2 – 2 So, find gof (x)…

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Q: Two polynomials P and D are given. Use  synthetic division to divide P(x) by D(x), and express P in…

A: The objective of the question is dividing the given polynomials.

Q: Match the vector field with its graph. F(x, y) = yi -5+ 1信 5 5

A: We have to graph the vector field of the given function

Q: B) Find for the Implicit function: dx x? – sin(xy) + y? = 5xy

A: The given equation is; x2-sin(xy)+y2=5xy.

Q: Find the general solution of the following nonlinear first order ariable separable O.D.E.: x?dy +…

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Q: 3 Evaluate lim et dt. e-t dt. 20 O a) -2 O b) 2 e O) 2 O d) 2 e e) None of these

A: Giveen query is to find indicated limit.

Q: Determine which graph corresponds to the area enclosed by the curves y = 3a and y = 2 + 2. 5- 8-…

A: Given the curves are  y=3x2 and y=x2+2.

Q: Find the inverse laplace of s+3 s2-8s-9

A: Given,  s+3s2-8s-9

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: Q2) Find the integral value for the following functions dx 4. S x2Vx2-1 eCos-1x 5. S V1-x2 6. Se…

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Q: 4x3 - 6 Find the differential dy of the function y = %3D 4 2x Provide your answer below: dy = dx *…

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Q: QUESTION 3. a) Find the general solution of y" - 2 --= 0

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