Verify the product law for differentiation, (AB)' = A'B + AB' where A(t) = B(t) = 1-t 1+t 41² 21³ 2t 2t - 1 ~|+ an

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A: We have given a trigonometric equation We have to find the values of A and B.

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Q: ·3 S S³ S² fő z dwdzdydx?

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Q: Qestion 2 a). Use vector projection to explain the distance in part (iii) equation b). find the…

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Q: Evaluate the following integral in cylindrical coordinates. 210 π 2 2 d²₁ dz r dr de 00-2 2 2 }}}. S…

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A: we need to solve the given questions and find the solution angle

Q: Evaluate the following integral in cylindrical coordinates. 379-x- 4 jjj 1 -3 0 01+x^+ 3√√9-x² 4 -dz…

A: The given integral is

Q: 37-42. Midpoint Riemann sums Complete the following steps for the given function, interval, and…

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Q: Differentiate implicitly to find ²-x²-22: (3-7) Then find the slope of the curve at the given point.…

A: We have to differentiate implicitly to find  Then find the slope of the curve at the given point.…

Q: 12. Find f. a. b. f(t) = f '(t) = 2 cos t + sec²t, -n/2 < t <π/2, f(π/3) = 5

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Q: Find the total differential U=-2t tan(7st)

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Q: (9) Given that g(x) = e(-), which of the following must be true on the interval (0, ∞)? (A) f(x) is…

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Q: Evaluate the double Integral Answer: 11,62 6ry dA, where D is the triangular region with vertices…

A: In this question, we will find the double integral.

Q: Consider the function f(x) = x²e¹0. For this function there are three important intervals: (-∞, A],…

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Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

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Q: 4. I-¹ 2 s² 4 (s + 1)ª

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

Q: Consider the following. S S SE 10xdV where E is bounded by the paraboloid x = (a) Describe the…

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Q: Kai is on an island 3 miles from the nearest point on a straight shoreline of the ocean, a town lies…

A: As per our guidelines we can solve one question only or first three sub parts only. If you need more…

Q: Differentiate implicitly to find dx x²y-2x²-4-0: (2.5) 2-0 The slope of the curve at (2,5) is Then…

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Q: For the function below, approximate the area under the curve on the specified interval as directed.…

A: we have given function

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

A: The expression of the second derivative of the function is given byTo determine: The expression of…

Q: Evaluate the integral: 1. √64 x² 14x² x = 64 tan(0) 64 sec (0) x = 8 sec (0) x = 8 sin(0) x = 64…

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Q: Find T5(x): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T5(x) = 1 2 2! +4…

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: Answer 1: The general solution of the homogeneous differential equation associated with the…

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Q: Given: (x is number of items) Demand function: d(x) 4563 √x Supply function: s(x) = 3√x = Find the…

A: For equilibrium quantity of the demand function, d(x) and the supply function, s(x) is when…

Q: Graph the polynomial P(x) = x³ + x² - 5x + 3 using calculus by showing the given steps: (d)…

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Q: Find the volume V of the solid below the paraboloid z=4-x-y and above the following region.…

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Q: Graph the polynomial P(x) = x3 + x²-5x + 3 using calculus by showing the given steps: (d) Determine…

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Q: Find the critical points of ƒ(x,y) = (x³y-y³) 5

A: To determine the critical points.

Q: You did not answer the domain. Please see  b) what is the interval of your interest (domain) for…

A: The objective function is

Q: 8. Let f(x) = x² - 3x + 1 and g(x) 2x² + 5x - 3. a. Find f(x) - g(x + 2). Simplify as much as…

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Q: Consider the triangle below (not drawn to scale). A ZA= b ZB= с C Let a = 10, b = 7 and ZC = 150°.…

A: a=10b=7Angle C= 150 degree

Q: A delivery company requires that any box delivered must have a length plus girth (distance around)…

A: Length of grithinWidth of grith  inHeight of grith in

Q: Consider the following initial value problem: y" + 81y = 98(t — π); _y(0) = 0, a) Find the solution…

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Q: A circular plate with radius 9 m is submerged vertically in water as shown. Express the hydrostatic…

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Q: Evaluate the following definite integral. Jo 0 F|+ ㅠ 4 3 sin x + 2 cos xd

A: The Sum Rule:The Constant Coefficient Rule:, where is the constant.And use the common integrals:

Q: (a) lim (ln(5x³ + 4) — ln(x³ + x + 7)) x→∞

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

Q: Tutorial Exercise An oil refinery is located on the north bank of a straight river that is 1 km…

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Q: Hello, how about 5-6, please? Thank you in advanced.

A: The first shift theorem :-Derivative property :-