Find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Focus F(0, -2) 4

Q: dw a) Find for the following function. dt w = 2ye* -In(z), x = ln(t2 + 1), y = cos(2t + 2), z = et…

A: If w=f(x,y,z) and x =g(t),y=h(t) , z=u(t) then,    dwdt =∂w∂x.dxdt+∂w∂y.dydt+∂w∂z.dzdt. Note : As…

Q: An integrating factor is μ(y) = The solution in implicit form is = c, for any constant c.

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. - 3. lim 1-3 (x − 3)…

A: limx→0 sin xx =1   and   limx→0 tanxx=1.

Q: V. Given: if x ≤ 2 el3r-6-2, [2x - 5], 13 f(x) if 2 3 √x²9, 1. Determine if f is continuous or…

A: Solution is given below:

Q: Find the radius of convergence of the power series. (If you need to use co or -co, enter INFINITY or…

A: Use the ratio test for checking the radius of convergence of series

Q: Let a = ci + j and b = 6i + 36j. Find c so that a and b are orthogonal. C = i

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: ☎ Q1: If x=² and y=21³ then b) 3 314 ² dx d) at x=4 F others Choose

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Q: 15 Give the properties for the equation 3y 2 - 2y + x + 1 = 0. Center (-1, 1/3) (-2/3, 1/3)…

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Q: Describe the long run behavior of f(p) = (p+ 2)(p+ 4) (p + 5): As p →→ ∞, f(p) → ? ✓ As poo, f(p) →…

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Q: • 1/2 dx x2 15. 16. dx [²2/ x6

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Q: if any. Find the absolute extremum point (s) of f(x) = el-cost on [-, π],

A: Given data÷

Q: IV. Do as indicated. 1. Let f(x): = where x = 1. 1 Find the equation of the tangent line to the…

A: Given equation f(x)=11+x2Differentiate…

Q: Revers the order and Evaluate= s dx dy y

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Q: limx→→∞ √1-x+2x+7 2 9x +5 - 3x

A: limit.

Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: Calculateri(t) r2(t)] and r₁(t) x r2(t)] first by differentiating dt the product directly and then…

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Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

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

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 10 ||ti + Pi|| dt = t²i||dt 1014.07 3…

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Q: Let f(x) = 31² - 20x + 25 2x² + 12 - 1 This function has: 1) A y-intercept at the point 2)…

A: Given that    f(x) = (3x2-20x+25)/(2x2+1x-1)

Q: 12. -s-7 (s+1)(S-2)

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Q: Find T(t) and N(t) at the given point. T(17) N() = ㅠ r(t) = 4 cos(t)i + 4 sin(t)j + tk; t = 2 =

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Q: Solve the differential equation and simplify (D^3 + D)^2y = 0

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: ست مارت منطقه مصرف سرت

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Q: Integrating Factor by Linear Equations: 3. (xy² + x²)dy + xydx = 0

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Q: What are the first 5 terms of the sequence a₁ = 5₂ a = 2n-a n-1, where

A: We have to apply simple mathematics logic to solve the problem

Q: 7. f(x) = 3√x; [1,4] 8. f(x) = x-2/3; [1,27]

A: We can solve this as follows:

Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√√x-1 1. lim x-5 x² - 4x - 5 2x…

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Q: 2. Let f(x)=√(2-x)². Use the local linear approximation of f(x) at xo = 1 to estimate √0.99 (1.01)².

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Q: Write TRUE if the statement is correct, otherwise write FALSE. Y y = h'(x) (-3,0) (3,0) x (0, -1)…

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Q: Match the function with one of the graphs below using horizontal asymptotes as an aid. 0.5- के 2…

A: Solved below

Q: nto v. t of u orthogonal to v.

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Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

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Q: Sketch a graph of f(x) 5 -5 = 4 3 -2 -1 12 1 -4 -3 3 Clear All Draw: Note: Be sure to include closed…

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Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1

Q: IV. Do as indicated. 1. Let f(x)= where z = 1. 1 ²+1 Find the equation of the tangent line to the…

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Q: y = tan-¹ (cosh x) (sin²x) (sech x) secz (use logarithm

A: We have to find dx/dy

Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Describe the end behavior (long run behavior) of f(x) = 28 As → →→ ∞, f(x)→ ? As I→ ∞, f(x) → ? v

A: This question can be solved using the concept of limits.

Q: Is Area = ∫βαf(x)dx∫αβf(x)dx as positive, negative or zero? positive negative zero

A: Here in first graph we had shaded the area under this function as given below in figure : So from…

Q: пр 4. STIS df x²s 5. Evaluat

A: I=∫0π3  x2 sin3x dxIntegration by parts;u=x2, v=sin 3xI=x2∫sin3x dx-∫(2x ∫sin3x dx)  dxI=-x2…

Q: Compute the area bounded by the curves x=2y² and x=4+y²

A: Area bounded by two curves x=f(y) and x=g(y) is given by, A=∫abf(y)-g(y)dy ,a,b are the points of…

Q: 314! What is the value of the expression 5! ? A 3 5 B 5 C 42 D 3,991,680

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -2x - (sin(x))² dy= Need…

A: Using derivative

Q: d d. Calculate[r₁(t) · r2(t)] and [r₁(t) × r²(t)] first by differentiating dt the product directly…

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Q: Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational…

A: Given: fx=36x2-12x+36x-3   As we know that; To calculate the vertical asymptote, equate the…

Q: Match the function with one of the graphs below using horizontal asymptotes as an aid. f(x) = 5+ H…

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Q: b. 36. Evaluate f(4x³ - 9x5 + 4x² - 6) dx. a. 32x7-45x + 8x + C 32x7 180x³ 4x9 C. b. 3 +8x + C…

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Q: Describe the graph of the equation. r=-13 i+(1-t2) j+t k O It is a parabola in the plane x = -13,…

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