If f(x, y) approaches 1 as (x, y) approaches (0, 0) along the path y = mx, where m is any real number, then lim f (x, y) = 1. (x,y)→(0,0)

Q: 23-24 Verify the linear approximation at (0, 0). 23. e" cos (ry) ze+1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: Solve the given differential equation. All solutions should be found. dy ° – 6y NOTE: Use c for the ...

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Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: he price, in dollars per units, that consumers are willing to pay for a popular high-end digital cam...

A: Price

Q: 1. Evaluate the following limits. 3x + 10 – 4 (a) lim 2--2- r2 – 4x + 4

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Q: Use substitution to evaluate the integral | (3x³ + 5)° . 27x²dx

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Q: Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by...

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Q: 21. Determine the general antiderivative of f(x) = 4x 4x4 + 9 2x2 a. 2 cosh +C 3 22 + C c. 2 sinh¯ -...

A: As per our guideline we are supposed to be answer only one question you can repost other question in...

Q: Find lim f(x) r→-5

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Q: Isin ()

A: 72sin(π5x) =75xnow here there are two curves  y =72sin(π5x) →(1) y=75x  →(2)solving by graphical met...

Q: Find a positive and a negative coterminal angle for each given angle 9) 285° 10) -225° 25T 11) 12) -...

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide ...

Q: 28. Evaluate eš dx and determine its particular antiderivative whose x-intercept is ln 3. 1 e3x – 3 ...

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Q: x³ + 3x dx. x2 + 1

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Q: V1+x3 dx [6] S (7) (ax2a (x2a+1)*dx x-2 ах2а (7] S

A: Given: (1)   ∫1+x33x-2dx (2)  ∫ax2ax2a+13xdx

Q: 2. / 3" csc²(3") sin“(3") da (3") sin®(3") dx

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Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second poli...

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Q: Solve the equation. 4k 45 e = 225 If 45 e 4k %3D = 225, then k= ||N (Type an exact answer.)

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Q: The gross domestic product (GDP) of a country is $78 billion and growing at the rate of 4.41-1/3 bil...

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Q: Management at a factory has found that the maximum number of units a worker can produce in a week is...

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Q: V1+x3 –dx r-2

A: ∫1+x33x-2 dx∫x2.1+x33 dx13∫3x2.1+x33 dx13∫3x2.(1+x3)13 dx

Q: 8. Find the maximum and minimum values of f(x,y) = x³y* subject to the constraint 5x2+ 2y2 = 14. 5x ...

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Q: » [3] S Te dx > Vex [4] S(x- s(x + !)° dx >

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Q: Find an equation of the line passing through the pair of points. (-5) ( 1) 4

A: The equation of the line is solved below.

Q: 3 V1+x3 -dx x-2

A: Given:      ∫1+x33x-2dx      =∫x2 x3+13dx substitute u=x3+1                 dudx=3x2→dx=13x2du

Q: Find the slope-intercept form of the equation of the tangent line to the curve defined by fla) = 3-2...

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Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1.

A: The equation of the curve is given by fx = 3x2-x-5 The point is x = 1 Formula Used: mtan = dfdxx=1 T...

Q: A fuel tank is being designed to contain 200 m3 of gasoline, but the maximum length of a tank (measu...

A: We have to find the height and radius of the fuel tank which costs minimum using differentiation.

Q: Evaluate the indefinite integral. 24 W cot(x) csc2(x) dx 24 cot?(x) + C 25 O (csc(x))24/25 + C 24 25...

A: To solve this use integration by substitution method

Q: 12. The time a person studies for a test is variation to success on test. an inverse a direct an ind...

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Q: 3. Solve for a: 2а + 4(а — 1) — 5 — (2а + 1) | а — a = a = 1 a = 0 2/3

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Q: -7 -1 3 5 -1 -2 -3 -4 ー5 -6- -7 -8- de your answer below: a. lim f(x) = xラ-6 5. lim f(x)= O

A: Given:   Graph is given

Q: dx x2 (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb in...

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Q: olve a nonlinear equation by making a change of the dependent var portant such equation has the form...

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Q: he differential equation (8 – r²)dr = %3D r² (1n (;) – = 0 cos cos = 0 (r+ 4) (in (;) –

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Q: V-x-2-V3 Evaluate lim -x- 5 Enter an exact answer.

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Q: cos(2x) -dx sinx+cosx

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Q: Determine the values of r for which the differential equation y" – 36y = 0 has solutions of the form...

A: We have to find the number of values of r which satisfies the equation.

Q: 19. The polynomial f(x) = (x – 2)3 = (x – 2)(x – 2)(x – 2) has æ = 2 as a zero four times. True Fals...

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Q: Find the length of the curve r(t) = for 3 < t < 16. Give your answer correct to two decimal places.

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Q: There is an infinite discontinuity at x = 0 and f(0)=-2

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Q: INTEGRAL Evaluate the following: 8. Se2×dx

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Q: Find the solution of the given initial value problem. cos t y%3D t 1 y' y(T) = 0, t >0 - t-1 y(t)

A: The given equation is; y'-y/t =cost/t-1; y(π)=0.

Q: Evaluate the following: 1. S(6x² – 4x + 1) dx

A: As we know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And ∫c·fx...

Q: A particular country's exports of goods are increasing exponentially. The value of the exports, t ye...

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Q: x²dx x³+ 4 3.

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: Differentiate. sin(0) f(0) 1 + cos(0) f'(0) %3D II

A: Differentiate 

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x = 4. dy ...

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Q: 1 2 Find the maximum and minimum values of the function - 6x + 8 - 2 2/3

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Q: 1.3 + j4 2. –3 + j4 3. –3 – j4 4. 3 - j4

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