Q1: find dx of the following statement: a) y = cos? sec

Q: | 5f(x)dr c f(r)dx if c =

A: Given :∫725f(x)dx=c∫27f(x)dx

Q: Use L'Hospital to determine the following limit. Use exact values. In r lim glnz

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Q: d. [r:(t) r2(t)] and r:(t) x r2(t)] first by differentiating d Calculate dt the product directly and…

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Q: S(Vcos x + sin x)´dx

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. If it…

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Q: Find the absolute maximum and minimum values of the function on the given curve. Function: f(x. y) =…

A: Let's find.

Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: Let g(x) = | f(t) dt, where f is the function whose graph is shown below. What is the value of g'…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Select the three reasons for the non-existence of lim,>c f (x). lim, c f (x) = 5 x→c lim, »c- f (x)…

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Q: t3 – 7t2 + 16t –- 12 t4 – 4t3 + 4t² 5. lim t2 w? – 4w + 1 6. lim w-00 3w2 + 7w – 4

A: limt→2t3-7t2+16t-12t4-4t3+4t2

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. %3D If u(1, — 3) — 7, и, (1, —…

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Q: 15 dy dt 2-

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Q: 4. Consider the matrix А 5 2 One of the eigenvectors of A is given by [1 -1]'. Find the eigenvalues…

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Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the sum of the series. 1 - In(4) + (In(4))² _ (In(4))³ 2! 3!

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Q: Evaluate the limit 5+ 9x lim 1+00 3 – 4x

A: Given problem:-

Q: 3. Check Euler's Theorem for the function f(x, y) = x + y3 + 3xy2.

A: Euler's Theorem for the function :          x∂f∂x+y∂f∂y = n.f(x,y) ; where , 'n' is the degree of…

Q: What is the lim,→1 4x 7 .? x+1

A: limx→1 4xx+1The function is defined at x=1.limx→1 4(1)(1)+1limx→1 41+1limx→1 42=2

Q: 2. S CoSx+sinx-1

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If th use co or -co,…

A: Given query is to find the series converges or diverges.

Q: Solve  x * (dy/dx) – x6ex = 4y

A: on solving this we will get :-

Q: FH is perpendicular to AC In the figure, AC is diameter. If EF = 3 and FG = 2. Find GH. E G EH is…

A: Similar triangles: Similar triangles are triangles with the same shape but different sizes. Similar…

Q: dw given w = a2 + 2y2 + 22 and a = cos (st), y = -2s Int and Use chain rule to find 2 = 3s' Vi.

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Q: Find r'(t). r(t) = (tan(6t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k. r'(t)

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Q: Solve the following second order homogeneous linear differential equation if the 4 initial…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Determine the vector field of F. F(1, y) = 9i – 3j

A: kindly attached following graph.

Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: xdx 46. S- V3+2x². – x+

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Q: Question 2 x2 Consider the function f(x) = x² –1 " (a) Find the intercepts of the graph of f (if…

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Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

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Q: Find V. (F x G), if F(x, y, z) = 14.ci + j+ 13yk and G(x, y, z) = xi + yj – zk. V· (F × G) :

A: Vector

Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: Let's find.

Q: Determine if the given series is absolutely convergent, conditionally convergent, or divergent. Show…

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Q: 1. Sam throws a stone into a river. This caused ripples in the form of concentric circles. The…

A: Given problem:- Sam throws a stone into a river. This caused ripples in the form of concentric…

Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: Consider F and C below. F(x, y, z) = (y²z + 2xz2)i + 2xyzj + (xy² + 2x²z) k, C: x = Vt, y =t + 8, z…

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Q: x-6x-4 dx x+2

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Q: Find the curvature and the radius of curvature at the stated poin r(t) = 11 cos(t)i + 10…

A: Here we have r→(t)=11cost i +10sint j +10t k  at=π2 The formula for curvature is…

Q: S tan -1x dx

A: Solution is done in step 2

Q: Solve the differential equation dy tan y x Cos x 3 dx

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Q: Show that the function f defined by (x, y) = (1, – 1) f(x, y) = 1² + y (x, y) # (1, –1) I + Y is not…

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Q: Which of the following is a parameterization of the line that passes through the point (1, –3) with…

A: First frame the equation then verify all the given option.

Q: by which criteria?

A: Apologies for the inconvenience. Here is the correct solution.   If a series ∑n=1∞an has either…

Q: Evaluate the limit 9х + 5 lim z+00 2r2 – 6x + 6

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Q: Evaluate the following limit using Taylor series. 7 7 tan -(x) – 7x + lim 4x° 7 7 tan "(х) - 7x +-…

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Q: Find div F and curl F if F(x, y, z) = 17y*z*i – 3x'2ºj – 3ry®k. div F= curl F=

A: Let's find.