Consider the parametric curve x = t² - 2t, y = t³ − 3t² + 2t. Find the equations of the tangent lines to the curve at all x-intercepts (i.e. points (x, 0) that cross the x-axis).

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A: As per our guidelines we able to solve only one question and rest of the question will be reposted

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A: Explanation of the answer is as follows

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A: Note: According to our guidelines, we can answer only the first problem or the first three subparts…

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A: The differential equation is given as  d2ydx2=10-24x , y'(0)=7 and y(0) = 9.

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A: r=-6cosθr=3  Find the point of intersection of the curve -6cosθ=3cosθ=-12θ=2π3, 4π3

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Q: Consider the function f(x) = 2x³ +39x² - 240x +9. This function has two critical numbers A B: and…

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Q: Question 3. Given the formula y(t)-y(t-h) h use the Taylor series y' (t) = h" "(t) ++ () (t) +…

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Q: ᎧᏃ at for z = f(r, s); r = g(t), s =) A) C) дz at ?z at = az dt dr dr əz dr dr dt + =h(t) əz dt as…

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A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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Q: Solve the differential equation by variation of parameters. 4y" - y = ex/2 + 6 y(x) = G₁e (x) + G₂e…

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Q: 4. Describe the long run behavior of f(t) = -5t6-2t4+3t³+2 As t-∞, f(t)→? As too, f(t) → ? ✓

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Q: 1. Find the following indefinite integrals a) √ √2-dx 5x e3t c) fdt b) fset - dt 3 2t d) fx²=1 dx 8x

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Q: Use the Chain Rule to find 54 72 w = x³y² + x¹z²+xyz, X = t² +e²t, dw dt y = 2+e-³t at t= 0 if and z…

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Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

A: Firstly we find local maxima or minima . secondly inflection point.

Q: Find the Maclaurin polynomial of order 3 (three) generated for f(x) = ex sin x.

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Q: 5) y = sec 0 2 Ma M Al

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Q: Question 8 find derivative of f(x). f(x)= 3x²-5x +1 O 6x+1 6x-5 О 6x 6x-4

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Q: x - 1 x² + 4x + 13 J dx

A: As per the guidelines we are only able to solve 1st question, and please upload the rest of the…

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Q: Differentiate the function. h(x)=ets. h'(x) = + In(x)

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Q: 8. Evaluate the limit by using a change of variable. 1 X6 1 d. lim x→l_x³ Vx 2 x4 √x³ - 8 e. lim 1…

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Q: Find all possible functions with the given derivatives. a. y' = 2x b. y' = 2x - 5 c. y'= 3x² - 2x -…

A: a y'=2x           b y'=2x-5           c y'=3x2-2x-5

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A: The given curve is: x(t)=e2t cos(t),     y(t)=e2t sin(t)       for  0≤t≤6

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Q: Write the expression as the cosine of a sum. Then simplify to write the expression as a…

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