Find the derivatives of trigonometric functions: y = 4 sin" x + 5 cos" x y = sin' x cos x y = 2 sec x + tan x 1+ tan x y = secx

Q: Find the area of the parallelogram that has u = 2i – 3j + 2k and v = 2j + k as adjacent sides. NOTE:…

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Q: 4y" + 25y = 0, y(0) = 3.0, y'(0) = -2.5 %3D %3D %3D

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Q: Σ n=1 (2n+ 1)3/2 Use the Integral Test to determine if converges or diverge:

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Q: Find the general solution of ydy/dx =2/(3x2). O a. y?/2 = 2/3x + C O b. y? = -4/3x+C O c. y/2 =…

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Q: The demand function for a product is modeled by  p = 400 − 4x,   0 ≤ x ≤ 100,  where p is the price…

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Q: 1. A small metal bar whose initial temperature was 20°C', is dropped into a large container of…

A: As per as our guideline i am supposed to answer only one question. please repost remaining question

Q: Vx2+16 dx X4

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Q: Let A be an eigenvalue of the n x n matrix A. Define A? to be the n x n matrix A? = AA. Show that X?…

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Q: (a)the curl and (b)the divergence of the vector field. F(x,y,z)= ln(2y+3z)i+ln(x+3z)j+ln(x+2y)k

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Q: 1. Find the eigenvalues and eigenvectors of the matrix. A = ( 3 -4 -3 2

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Q: Given the piecewise function |x² + 1, if x > c f(x) = | 2æ, 2x, if x <c lim f(x) exists find the…

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Q: Evaluate the integral. dx a > 0 (a² x3,3/2' Need Help? Watch It Read It

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Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

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Q: Find the area of the region bounded by y = 2x , y = -8x and y = 2 %3D using double integral. Leave…

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Q: 10. | xSin4xCos4xdx

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Q: A table of values of an increasing function f is shown. 10 14 18 22 26 30 f(x) -11 -5 -4 3. 30 Use…

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Q: Find the average value of the function over the given interval. (Round your answer to four decimal…

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Q: E 2na". n=0 Based on the Ratio Test, which of the following conditions on x will guarantee that the…

A: Ratio Test : Suppose we have the series ∑ an . Define,                         L = limn→∞…

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

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Q: Water flows into an empty reservoir at a rate of 2200 + 15t gal/hour . What is the quantity of water…

A: Given, Rate of  flow into the tank= 2200+15t gal/hour t is time in hours Time= 6 hours

Q: -1 Cos'x 4. | X. dx 1-x* 2 dx 3 (x² + 2 + 2x + 2)2 5.

A: 4). Given: I=∫cos-1x1-x2dx    ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Find the derivative if the following and simply to its simplest fo a) y= (4t2 – 3t + 2)-2 (x+3)* b)…

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Q: Evaluate the definite integral. Use a graphing utility to verify your results. 25 dx

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Q: Sketch the graph of a function f that has a local minimum value where f'(a) = 0. Choose the correct…

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Q: For each equation, determine whether it represents a direct variation, an inverse variation, or…

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Q: The function f(x)= x^2 - 6x+4 on which interval will f(x) have a root?

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Q: Approximate the area of the region bounded by the graph of f(x)=16-x and the a-axis on the interval…

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Q: Using the graph, determine the values of c such that  (please see the attached photo) exists,…

A: Solve the following

Q: In(y) Evaluate the iterated integral: ye 4xdxdy. Show all of your work.

A: To evaluate the iterated integral. ∫12∫0lnyye4x dx dy

Q: Find the intervals on which fis increasing and the intervals on which it is decreasing. f(x) =…

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. 4X-1 e lim…

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Q: Find the center of mass (in cm) of the partices with the given masses located at the given points on…

A: Given: The mass and location of the particles.

Q: (y-3)/(x³+1) dy = y4dx is a separable differential equation. Select one: O True O False

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Q: the graph of the function f(x)=1/x+3-10 is a transformation of the graph of the function g(x)=1/x by…

A: f(x)=1x+3-10  , g(x)=1xConsider g(x)=1xHorizontal shift left  by 3 units⇒g(x+3)=1x+3Then Vertical…

Q: Encontrar el enésimo término de las sucesiones 1 2 3 4 4'9'16' 25 3n an 1 1 an (n + 1)! °n =+ (n +…

A: Consider the sequence  14,29,316,425,........

Q: (x + y)dx + (x – y) dy = 0 %3D

A: A detailed solution is given below

Q: (x²–2x)° 2. у %3 x2 Differentiate using Logarithmic Differentiation

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Q: Find a power series for f(x) = In(1+ x). Hint: In(1+ x) is one antiderivative of (whose 1+x power…

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Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

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Q: dx 6. xVa² - x² X

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Q: that you are using. Σ n=1 n/2+1 •a.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Use polar coordinates to find the volume of the solid region that lies inside the sphere x2 + y2 +…

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Q: The drawing below shows a right-angled triangle. A straight line crosses the triangle parallel to…

A: We have to find an equation for the length z.

Q: Here is a graph of the function g. Use the graph to find the following. If there is more than one…

A: We can answer both the question as below.

Q: At each point (x,y) on the curve, the slope is 2x+1. The curve passes through the point (-3,0). Find…

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Q: Find the area under the graph of f over the interval [- 2,3]. 2 X +4 X 1 The area is (Simplify your…

A: Area(A)=∫-21(x2+4)dx+∫135xdx

Q: 13. Integrate: S(sec³ 0 tan 0 - sec 0 tan³ 0)d0 A. In sec 0 + C В. In sin @ + С C. sec 0 + C D. sin…

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Q: 2(2x? + у?)dx — ху dy %3D 0

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Q: 7. SE (x? – 2 +) dx = x(x³ – 4x + 4) + C 8. S(cot?x + 2)dx = x – 2+C cot³x 9. S csc²x D dx = - ot'x…

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Q: Let f(x) = sin(x). Use the formula for the nth coefficient of the Taylor series for f(x) = sin(x)…

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