Find the derivative of the trigonometric function. y = sin((πx)8)

Q: dz Find when u = 0, v = 3, if z = sin (xy) + x sin (y), x = 3u² + v², and ди y = 2uv.

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Q: Find the derivative of the function. F(0) = arcsin (√ sin(150)) F'(0) =

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Q: Differentiate r(t) = (cos(t)², sin(t)², t³).

A: The given vector valued function

Q: Describe verbally the transformations that can be used to obtain the graph of g from the graph of f.…

A: we are given two functions, we need to write down the transformation that f(x) should undergo in…

Q: A rectangular beam is cut from a cylindrical log of radius 50 cm. A cross-section of the log is…

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Q: Show that the function y= x ln x is a solution of the differential equation xy" - y' + (1/x) y = 0.

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Q: Suppose f (x, y) =x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: Show that the function is increasing on the given open interval. (Enter your answers as a…

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Q: 4. A water tank in the shape of an inverted cone has height 92 cm and radius 60 cm. If the water…

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Q: Use upper and lower sums to approximate the area of the region using the given number of…

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Q: 2. Find the derivative: a. y=ln(e^x)/(1+e^x)

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

Q: Use implicit differentiation to find dy/dx of tan(x+y)=2y

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Q: Write the equation 52 = 25 in logarithmic form.

A: Write the equation  in logarithmic form.

Q: Let f (x) = - x² – 3. Find and simplify ƒ' (x) and ƒ" (x). x5 f" f'(x) = A = -3 B C = || f" (x) D E…

A: Given Function f( x ) as follows

Q: Use the quadratic formula to solve the equation. Give two forms for each solution: an expression…

A: The given quadratic equation is

Q: Compute the following limit using L'Hospital's rule if appropriate. lim (√2³-42² - 2) = I->∞0

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Q: If f(x) = f'(x) = ƒ'(1) = = 2 sin x 3 + cos x > 3 cos (1) () then 3 cos (x) + sin(x) (3 + cos x)² X…

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Q: Find the surface area of the surface given by the portion of the paraboloid z=x^2+y^2  that lies…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6, 1) y…

A: The tangent to a curve at a point is obtained by finding the slope at that particular point using…

Q: Evaluate the integral by converting to polar coordinates. 2 √8-y2 S² S Y 1 √1+x² + y² dx dy= = 16pi

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Q: Evaluate the following limit. lim x→0 3 (²2 x 3 sin(2))

A: L=limx→0(3x−3sin⁡(x))

Q: d Find ax(-3x-4).

A: We need to find the following derivativeFormula Used:

Q: Two sets A and B are defined as follows: A = {x, y, z); B = {1, 2, 3}. Ug Oh f range of g range of h…

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Q: HOMOGENEOUS DIFFERENTIAL EQUATION Solve the following differential equations using HOMOGENEOUS DE.…

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Q: Find the square root of 7225 with the modern method

A: A number's square root is a value that, when multiplied by itself, returns the original number.

Q: 1. Consider the following function, if x # 0 if x = 0 Prove that the function f is differentiable at…

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Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the…

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Q: Labor. Refer to Table 4. (A) Find the average rate of change of weekly hours from 1980 to 1990.…

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Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

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Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:…

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Q: Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by…

A: Given that, where R is the region bounded by the graphs of                  Using the change of…

Q: H.W/ Maximize QuiZ 1/ 2= 80×1+ 60 X ₂ X₁ + X₂ 15 100. subj to: + X₂ 15 150 X₁ + 10X₂ If Boo الاحدا

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Q: Find a graph up and down from the equation g (x) = (x + 1) (x-2 )

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Q: Find the derivative  a. y= ln(cos^2x) b. y= e^cosx+e^-x

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Q: Consider the following. Find y'(x). y'(x) = y = X = X x² +9 Find the critical numbers of y(x).…

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Q: If 6 J of work is needed to stretch a spring from 12 cm to 14 cm and another 10 J is needed to…

A: Work = 6jAnother work =10j

Q: Let g(x) = ² + 12 Ax² + B (x²+12) C A = B = C= = D = E = F = g"(x) = x(x² + E), where (+²+F)G where…

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

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Q: Let f(x) = Then f'(x) = π The equation of the tangent line to y = f(x) at a = can be written in the…

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Q: 2. Determine whether the series n Σ» (-1) (3) converges or diverges. If it converges, find the sum.

A: The given series is

Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2…

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Q: (a) Consider the curve y = x - 3x7. d.x (b) This function is not differentiable when = (c) (Give…

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Q: Question 6: For each of the following functions f, find its natural domain. (a) f(x) = 22-2-3 (b)…

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Q: Is the series convergent or divergent? If convergent, is it absolutely convergent? cos (πn) e-n COS…

A: Consider the series

Q: Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on…

A: To find the upper and lower sums for the region bounded by the graphof the function and the x-axis…

Q: Consider the function f(x, y) = (4x-x²) (2y - y²). Find and classify all critical points of the…

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Q: A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well that is…

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Q: Extrema on a sphere Find the points on the sphere x² + y² + z² = 25 where f(x, y, z) = x + 2y + 3z…

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Q: 2. Given the following tetrahedron, name the following: a. Vertices b. Edges c. Faces

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Q: ROBLEM No. 1. Solve the IVP: y"+6y-7y=0, subject to the initial conditions: y(0)=5; y '(0)= -3.

A: Given Differential equation is as follows