Find the slopes of the surface in the x- and y-directions at the given point. h(x, y) = x2 − y2 (-2, 1, 3)

Q: Question 5 Test the series below for convergence using the Root Test. 5)₁ ∞ n=1 f(n): 3n 6n + 5 The…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: Q5/ find the Fourier expression of f(x). f(x)=x+x² for _π< x <π -

A: I have done solution step by step in detail....go through the solution

Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³ (2)y=tan³ √/cot(7x); (4) y = x sinh…

A: Solution is given below:

Q: Evaluate the indefinite integral as a power series , x² ln(1 + x)

A: We want to find the indefinite integral as a power series.

Q: Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die…

A: The objective is to solve the above question.

Q: 3): Find the tangent equation to the curve y = sin² x at point x =

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Q: 11. f -dx 3x+1 +4x

A: these 2 questions are not related to each other so according to bartleby guidelines I need to solve…

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: Given the function f(x) = x² – 3x f(2+h)-f(2) h (a) Find the expression (b) Use your result from…

A: The given function is ; f(x)=x2-3x.

Q: If R is the region bounded by the graphs of the functions f(x) = 2 + 5 and g(x) = x + ½ interval [1,…

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Q: Let g(x) = = f(1) dt, where f is the function whose graph is shown below. At what value of x does…

A: Given: gx = ∫0xftdt Using Leibniz integral rule, we get g'x = ddxxfx -  ddx0f0 g'x = fx

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim→∞ 2n+1 log10 (3x -…

A: The objective of the question is fill the blanks.

Q: 7 [[11x + √]dx = [ 8x3 +C

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Q: Q2/ A. Find the following limits. Answer four only. i. ii. iii. iv. V. lim x1 x-1 4x-x² lim X-4…

A: To evaluate the limit.

Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: · 1. -1 (3-2x) ³ dx

A: The objective is to evaluate the integration.

Q: 818 B. Find the horizontal, vertical, and oblique asymptotes of the curve y =

A: In this question, we want to find the vertical, horizontal and oblique asymptote of the given curve.…

Q: Evaluate the following integral. π 2 7y sin y s s dx dy 0 0

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Q: (B): If A = 2i + 3j-4k; B = 3i-4j+ 5k and C = i + j-k, find: (iv) (3A + 4B). C (1) A.B (U) B.C (iii)…

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Q: Find all the zeros. Write the answer in exact form. n(x)=x³-7x² +13x-3 If there is more than one…

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Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

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Q: 3. Find the volume of the solid formed by y = √√4sin(x) bounded by x = 0 revolved about the x axis…

A: According to the question we need to find out the volume of revolution of the curve.

Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

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Q: Given: f(x) = 0.2 + 25x-200x^2 +675 x^3-900 x^4 + 400 x^5 from a = 0 to b = 0.8 and segment equal to…

A: Given that      f(x) = 0.2+25x-200x2+675x3-900x4+400x5   from a=0 to b=0.8 and segment equal to 8.…

Q: Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo…

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Q: (C): If w = tan x and x = 4²³ +t: Find?

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Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³; (2)y=tan³ √/cot(7x); cash? -nh.…

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Q: (B): If A = 2i +3j - 4k; B = 3i-4j+5k and C=i+j-k, find: (ii) B.C (iii)A. (B+C)and (A + B).C (iv)…

A: Given: A→=2i+3j−4k;B→=3i−4j+5k and C→=i+j−k We know that x1i +y1j+z1k·x2i +y2j+z2k = x1x2+y1y2+z1z2

Q: Find the sum of the series. 5(-1)^²n +1 Σ 62n + 1(2n + 1)! n = 0 62n +

A: The sum is evaluated below.

Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² - y² O O X x

A: Given that       f(x,y) = e1-x^2-y^2

Q: Find dy x 3 In (x - y) = xy + y²

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

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Q: Q3/ Solve the following Second order differential equations. 2- d²y dx² +3+ 2y = e-x + e-2x -

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Q: -9 (x-1) 8. √x dx

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x A 1.

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Q: 2 x²log₂ (x) dx S

A: Please show complete solution. (Use integration by parts)

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: We have to find out equation of tangent

Q: Evaluate the function at the given values of the independent variables. Simplify the results. g(x,…

A: We can solve this as follows:

Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

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Q: 10.¹ (3x² - y²) dx + (xy − x³y¯¹) dy = 0 2 du

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Q: If A, B, and C are 3×3 matrices; and det(A) = 5, det(B) = −2, and det(C) = 3 then compute: det…

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Q: Use the tabulated values off to evaluate the left and right Riemann sums for n = 10 over the…

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Q: dw (C): If w = tanx and x = 4t³ + t ; Find dt dy

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Q: Describe the level curves of the function. z=x+y, c= -2, 0, 2, 3 O The level curves are parabolas.…

A: We need to choose correct option.

Q: Use the substitution u= x² + 6 to find the following indefinite integral. Check your answer by…

A: To evaluate the integral.

Q: Sketch the space curve. Function r(t) = (5 sin t, 3t, 5 cos t) 1.0 0.5 0.0 0.0 -0.5 -1.0 -5 N 0.5…

A: Please see the below picture for detailed solution.

Q: At least one of the answers above is NOT correct. where a 9 and b = 7 1³h 10x² - [ 1(a) dx = f* f(x)…

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Q: 7. 0 , e5) a dx

A: Please see the below picture for detailed solution.