← dy (a) Show that y* +x-6=0 is an implicit solution to dx Part 5 of 6 1 on the interval (-∞,6). 4y (b) Show that xy5-xy5 cos x = 1 is an implicit solution to the differential equation dy (-xsin x + cosx-1)y on the inton. (0.2

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A: Topic = Functions

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Q: X 16. Determine the equation of the tangent to the curve y=30* at the point with x-coordinate.

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Q: 1. Use trigonometric substitution to evaluate the integral √9-x

A: We need to solve integral.

Q: 9. What is the slope of the normal to a. -3 y = x²-1 x+5 at (1, 0)? Show your work. C.

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Q: 44. Simplify: cos 40° cos 30° + sin 40° sin 30° 45. Simplify: cos 50° cos 20° + sin 50° sin 20⁰

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Q: 9) The sequence a₁ = a) Diverges b) Convergest c) Converges to 15 2 d) None of the above 4n²+1

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Q: d the open intervals where the function is concave upward or concave downward. Find any inflection…

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Q: 4. Trace the curve: y² = x²−4x−12 x²-2x-3

A: for x intercept put y=0for y intercept put x=0y2=x2-4x-12x2-2x-3

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Q: d) xy' + (1+x)y=e* sin(2x)

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Q: 18) The graph of f(x) is shown. fox A) I only 4 B) 1:4 f¹=0 at X = ? c) 1; 4; 5: D) 143536

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Q: Solve the initial value problem dy € + ² = 5x√ỹ, _y(1) = 2.

A: standard form is dydx+p(x)y=q(x)given  dydx+yx=5xydivide by y  both sides 1ydydx+1x×yy=5xwe know…

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Q: If ["F(x) 1.2 f(x) dx = 7.2 and nd ["fix) dx = 5.6, find [° F(x) dx. X

A: we know that ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx, where c is betwwen a and  bgiven  ∫17f(x)dx=7.2 and…

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A: Given the integral is ∫9x2-9x dx

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Q: Which of the following does not test for divergence? O The integral test. O The root test.

A: We are asked to find the which of the following does not test for divergence

Q: b) (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

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