Find the derivative of y = arccos x + x 1-x²

Q: 6. Find the values of at which the graph of f(x) = = 4x² - 3x + 2 has a tangent line parallel to the…

A: Follow the procedure given below.

Q: 2. f (x²-16) ²/2 dx x3

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Q: Consider the following. w = x - ¹₁ x = e³t, y = t³ (a) Find dw/dt by using the appropriate Chain…

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Q: u⃗=5i⃗−j⃗− k; v⃗=−i⃗+5j⃗+8k.  Find the projection of u ⃗ onto v :⃗

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Q: Find the angle of inclination of the tangent plane to the surface at the given point. (Round your…

A: Find the angle of incidence of the tangent plane to the surface of the given point.

Q: Evaluate the given integral: 2 fлсoе² (2x) dx

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Q: The directional derivative of f(x, y) = -xe²y – x³y at the point (0, 4) in the direction of the…

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Q: x(t) = £−1 x(t) = L−¹ S s² +5 3s² +9 4s ((s + 3) (s+5))

A: Last 2 question solved

Q: The value of the integral is: b 12 f(x) dx = a

A: Given that the graph of the function  To find the definite integral that represents the shaded area

Q: The result of the integral is equal to 4 √ = (x − 1)(x + 1) dx

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Q: Consider the initial value problem (a) Solve the initial value problem. (enter yo for yo). y(t)= y'…

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have…

Q: True or False: If / (x − 3)(x + 2) - then B = Select one: O True False 2 5 -dx = 3 - In(|x − 3]) +…

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Q: 5. Use the definition of Taylor series to find the first four nonzero terms of the Taylor series for…

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Q: Answer the questions for the function f(x) = 3x - 24x³ C УР f'(x) = 12x - 72xX f''(x) = 36x²-144x…

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Q: Part b: (**) We consider the function f(x, y) = x sin y - y cos x + y Find fx(x, y), fxy(x, y), and…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Several terms of a sequence {an}=1 are given below. 5, 5 5 5 5 6' 36' 216' 1,296 a. Find the next…

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Q: For a given cylindrical tank, the radius is 2m and the height is 18m. The tank is filled to a depth…

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Q: 3. A 20 ft ladder is leaning against a wall and begins to slide. How fast is the top of the ladder…

A: A 20ft ladder is leaning against a wall and begins slide.The ladder is 12ft away from the wall and…

Q: Consider the following function. f(x) = (x - 3)ex (a) Find the critical numbers of f. (Enter your…

A: We have to find the critical points, monotone intervals and relative extremum.

Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

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Q: 7. (a) Use the Maclaurin series cos x = 8 k=0 (-1)^2k (2k)! (b) Use the Maclaurin series ln(1 + x) =…

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Q: Find the normal vector to the level curve f(x, y) = c at P. f(x, y) = -2x - 3y c = 4, P(0, 0)

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Q: Choose all critical points of the function f whose gradient vector is Vf(x, y)= ○ (0, 2) O None of…

A: We have to choose correct option for all critical points.

Q: Let f(x, y, z) = yexyz², then fxz is: Select one: O (4xyz + 2x²y³z²)exyz² O None of these O (2xy² +…

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Q: 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1 - 12 21 √12 - 4

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Q: The graph of the first derivative f' of a function f is continuous on (-∞0,00). -2 -1 2 3 (e) Find…

A: The graph of the first derivative f' of a function f is continuous on -∞, ∞. e To find the…

Q: if: z = cos 0+isin prove that: 1) 2+1 z+1 2)221 +1 = itan 0 z² = Z

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

A: Here we have to find the directional derivative.

Q: A company manufactures two types of bicycles, a racing bicycle and a mountain bicycle. The total…

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Q: Find the point(s) on the surface at which the tangent plane is horizontal. z = 3x² - y² + 4y ) (x,…

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Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1,-1).

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Q: 7. Use the graph to determine the intervals on which the function is increasing, decreasing, or…

A: 7)  from given grap  (oo ,-2] decreasing and [-2,oo) increasing Minimum at x=2 value is -2 8)(oo…

Q: Two poles are connected by a wire that is also connected to the ground between the poles. The first…

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Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

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Q: Integrate the given function (Handwritten) tan2x + 2x^2x

A: Here we use basic formula of integration .

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive.…

A: This question is based on Lagrange multiplier.

Q: Integrate S 2x² (x − 1)(x² + 1) de using partial fractions.

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Q: Find the general solution of the differential equation. y (4) + 2y" + y = 9+ cos(4t). NOTE: Use C₁,…

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Q: Consider the function f (x) = x³ -12x^2 + 36x = x (x-6)^2 to answer the following questions.   1.…

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Q: Evaluate the integrals using trigonometric substitution dz 2² √2²-4

A: Find the inegrals by Trignormeric substitution

Q: Solve the following first-order linear differential equations. Simplify your answers. dy dt y = 0,…

A: We can answer the questions as below.

Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = z =

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: Solve Problem 346 in section 4.7 of the textbook. In addition to providing the calculations, draw a…

A: Solution is given below:

Q: -(4x³y - 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is exact. B) Solve the…

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Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: 3) Consider the DE: -(4x³y - 16)dy = (6x²y² - 10)dx. A) Show that the differential equation is…

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Q: Which of the rectangles below are both left and right rectangles? 10- 8- 6- 4- 2- 0- 0 8 CD 0000 05…

A: Rectangle which is both left and right rectangle is the rectangle which touches the function from…

Q: Consider the indefinite integral fe5z +6 dæ: a) This can be transformed into a basic integral by…

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Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(3x) cos(11y) has the…

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