Q3: A) Find (dy/dx) for: y² cosh(x+y)+ (tan(x)) sin(y) = eln(xy)

Q: Find the equation for the plane through the point Po= (8,3,3) and normal to the vector n = 5i…

A: Given that the plane passes through a point  and normal vector

Q: Find a unit vector in the direction in which f(x, y) = 5 cos(5x – 3y) ㅠ P07 ), and find the rate of…

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Q: 9 Find the linearization of f(x) = x at a = 8. Use it to approximate 8.1 (Show your work)

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Q: . a) Write an equation for a family of even functions with four x-intercepts, two of which are −1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: OABC is a rectangle and the two shaded regions are equal in area. Find k. Ay D A k [y=x²+k B C 2 X…

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Q: Use a power series to compute lim x-0 x³-3x+3 tan-¹ x -1 x5

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Q: - Find a unit vector in the direction in which f(x, y) = 5 cos(5x – 3y) decreases most rapidly at…

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Q: 4. Evaluate the following indefinite integrals. When you get an answer, you do not need to simplify…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the following integrals. If you use trigonometric substitution, please simplify using the…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. cos(x) Σ…

A: By using a Maclaurin series to obtain the Maclaurin series for the given function.

Q: Find the sum of the series. 8 Ë (-1)^2n n = 0 42n(2n)!

A: To find the sum of the following series.

Q: Show that F is conservative and use this fact to evaluate F.dr along the given curve: F(x,y) =…

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Q: for the graph answer question a-d

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Q: 8 S ( ² − 5 + £ ) da 6 dx X x² x³

A: I=∫(8x−5x2+6x3)dx

Q: The First Gate Having crossed the room, you find yourself at another gate with a required passcode.…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 2x²…

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Q: For the given function f(x) and values of L, c, and e> 0 find the largest open interval about c on…

A: Given:

Q: Find the area of the triangle determined by the points P, Q, and R. Find a unit vector perpendicular…

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Q: Solve the following initial value problem over the interval from t = 0 to where y (0) = 1. dy dt…

A: Solution is given below.

Q: Show that the line integral is independent of path. Jo 2xe-Ydx + (2y = x²e-⁄)dy, C is any path from…

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Q: 6 In Fig.11.23, the curve (y - 1)² = x + 4 meets the y-axis at A and B. (a) Find the coordinates of…

A: In the following figure, the curve  meets the y-axis at A and B.(a) To find the coordinates of A and…

Q: A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on…

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Q: Find f" (x), if f(x) = 4 sin(2(x + 1)). O 8 sin(2(x + 1)) O-16 sin(2(x + 1)) O-16 sin(x + 1) O 8…

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Q: Evaluate the following limits. If needed, enter int lim √9+4x2 2+6x x →∞ lim <X √9+4x2 2+6x Mention…

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Q: Consider the following separable differential equation (a) Write this equation in the form [P (y) dy…

A: Given Differential Equation

Q: Find a unit vector in the direction in which f(x, y, z) = x³z²+y³z + z − 1 increases most rapidly at…

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Q: can you solve part (d)

A: The given integral

Q: Use the given graph to find the largest value of 8 >0 such that for all x, f(x) - L<e whenever…

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Q: Suppose the daily supply equation for noise cancelling wireless headphones is given by P = S(x) = 70…

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Q: Consider the following limit of Riemann sums of a function f on [a,b]. Identify f and express the…

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Q: A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters…

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Q: lim, 1 1+7z 1+2z²+524 3

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Q: π sinx - sin(x) x+0 x cos x - x cos(x) Problem 2: Evaluate lim

A: given limit

Q: Let g(x) = 2x² + 8000 g"(x) = 4+ x3 4000 " + 10 with first derivative g'(x) = 4x - X and exactly one…

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Q: Consider the trapezoid whose bases are the left and right sides of the shaded region. The trapezoid…

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Q: 1) Evaluate the following triple integral: 1 xx+y IT 01 0 6z dzdydx

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Q: f f(x,y) = 4x² + 8xy−48x-8y

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find a basis for the kernel of the linear operator: T(x, y) = (6x - y, -24x + 4y) NOTE: Using the…

A: Given,

Q: Evaluate yz dx - xz dy + xy dz, where C is the curve x=e¹, y=e³¹, z=e¹, 0≤t≤1

A: To evaluate , where  is the curve .

Q: 2. (a) The region in Figure 8.34 is rotated around the x- axis. Using the strip shown, write an…

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Q: Problem 4: Let en = 2.4.6. (2n), the product of the first n positive even integers. Use the Ratio…

A: en = 2.4.6.........2n

Q: Evaluate: ²dz dy dx Oπ/48 π/96 π/24 O tan-¹(2)/24

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Q: 2 Find the equation of the tangent line to the given curve at the specified point: (Show your work)…

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Q: 3. (a) The region in Figure 8.35 is rotated around the y- axis. Using the strip shown, write an…

A: We have to write an integral for volume and evaluate it.

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: the region is rotated around the y-axis. Write, then evaluate, an integral giving the volume. a)…

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Q: Give a geometric description of the set of points in space whose coordinates satisfy the given pairs…

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Q: Evaluate the Evaluate ax + b lim Ia x² + c algebraically. giving your answer in exact form. Answer:…

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Q: 2² 2! 2 x 24 4! 4 x + 26 6! 26 28 # + 8! %e = 1 - 2

A: 222!x2−244!x4+266!x6−288!x8+⋯=12,x∈[0,π]

Q: a B b с Α)

A: a=8 and b=5Using Pythagoras Theoremc2=a2+b2c=64+25=89