Consider the curve y = x - x³. (a) Find the slope of the tangent line to the curve at the point (1, 0). (b) Find an equation of the tangent line in part (a). y =

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Q: (d) lim x→0 cos(a + x) cos(a — x) * (e) lim x48 * (f) lim xxx 2x - 1 2x + 1 X x In(e³ + 3) In(e5x +…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

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Q: Suppose v₁ and v₂ are vectors with |v₁|= 2, |v₂| = 3, and v₁ v₂ = 5. Let

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Q: 6) 3x² = 7x + 20 -3x²-3x²

A: given information

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Q: If a rock is thrown upward on the planet Mars with a velocity of 19 m/s, its height above the ground…

A: Since you have posted multiple sub-parts in the question, as per guidelines, we are supposed to…

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Q: 8. u = i- j + k, v=i+j+ 2k

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Q: IF g(x) = sin(x), then g'(x) = cos (x) 9₁ (3) = IF F(X) = (sin x + 8 cos x, then F'(x) = 6 COS (X) -…

A: Since you have posted a question with multiple question, we will solve first two question for you…

Q: If f(x) = 5 sec (3x), find f'(x). 15 sec (3x) tan (3x) Find f'(3).

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Q: Based on the definition of Fundamental Theorem of Calculus, what instances in your definite life…

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Q: 6. Solve the following initial value problems and verify your answers, dy = 3x²e; y(0) = 0 dx

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Q: |u| = 7, |v|= 3 and u⚫v = 4. Find |2u + vl. Find lu - 3vl. Find λER such that (u - λv) Lv.

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Q: Find the work required to pump all the water out of a cylinder that has a circular base of radius 5…

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Q: 4. Find the bounded area between the curves. Draw the region. y = -cos2x 1x1 = 1/2 I x=1-sin2x

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Q: 5. Use the limit definition of derivatives to compute f'(x), where f(x) that a, b, c are constants.…

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Q: A sample data set has a mean of 72 and a standard deviation of 12. Determine whether each of the…

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: Find the area of the shaded region. AY 2+ L -3 + + 2 3 square units y=x-2 34 y=√x ✈X

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Q: Suppose h(x) = f(g(x)). Given the table of values below, determine h' (2). x f(x) g(x) ƒ'(x) g'(x) 2…

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Q: find the derivative by using the product and or quotient rule  g(w)=e^w(w^3-1)

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Q: d 4. Determine sin√x dx Space on next page in radical form]

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Q: 2. Find the LU factorization of the following matrices without pivoting 2 3 1 b) A= a) A = 2 5 354 1…

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Q: Find the general solution of the differential equation. y (4) - 34y(3) + 289y'' = 0 y(x) =

A: To find the general solution of the following differential equation.

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Q: A total-cost function is given by C(x) = 1700(x² +5)¹/³ +800 where C'(x) is the total cost, in…

A: the given cost function C(x)=1700(x2+5)(1/3)+800 , for the production of x airplanesrate of change…

Q: 2) Given the function f defined by f(x) = 7√⁹x²-1

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