Q3 : prove that : cosh?x + sinh²x =coch2x

Q: Find div F and curl F if F(x, y, z) = 17y*z4i – 3x°z®j – 3xy°k. - div F= curl F=

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Q: We want to fenca in a ne slide b up againd a lacae building and Idbesn't noedh fancing rechanguler…

A: This question can be solved using the concept of maxima or minima.

Q: OMMU a) Find the exact area of the shaded region. b) Use the calculator to approximate to the…

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Q: 3 10. S 2x Vx2 – 3x + 1

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Q: Evaluate the defınite integral. 8 i + e¯´j+tk)dt 0, – (e-1 – 1) j+ k i-e'j+;k 8 (e* – 1) i – (e- –…

A: The given integral is: I=∫01e8ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: x² Consider the function f(x) = x² –1 (a) Find the intercepts of the graph of f (if any). (b) Find…

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

Q: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

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Q: 1 In AFDE, d= 4 ft, e = 5.5 ft, mZF = 24°. Find the area of the triangle and round to the nearest…

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Q: Find V (V x F), if F(x, y, z) = 6ei+ 9xe'j - 5e k. V. (V x F) = %3D

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

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

Q: S tan -1x dx

A: Solution is done in step 2

Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

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Q: 2. S CoSx+sinx-1

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Q: V3x - 2 lim tan- %3D x + V3

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Q: alyze and sketch a graph of the function. Find any intercepts, relative extrema, and points of…

A: We are allow to solve one question and 3 subpart only at a time. If you want rest of solution please…

Q: Зx* у + tan y dy Given a first order differential equation dx Q3 x' +xsec? (a) Clarify the exactness…

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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: Solve  x * (dy/dx) – x6ex = 4y

A: on solving this we will get :-

Q: -+14х+13 dx 3x х+4

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Q: 15. Evaluate the following double integral. Si (xy* + x)dydx

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Q: The arc y = x² from (0,0) to (2, 4) is rotated about the y-axis. Find the area of the resulting…

A: We want to find surface area

Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: A Find the area bounded by the curves, the axis and the given values of x. Sketch the graph. 1.…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 1 5. Let f(x, y) = x² 6y3 - In y ), for y > 0. af of f &²ƒ Əx' dy' Əx²' dy²' Determine the partial…

A: Given: fx,y=x216y3-lny   As we know that; The Power law: ddxxn=nxn-1 And ddxlnx=1x

Q: show

A: As per the guidelines we can solve 3 parts only.

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

A: This question can be solved using the concept of domain and of functions and value of a function at…

Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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Q: 3. Let f(x) = x (x² + 1)/2. (a) Evaluate fo f(x)dx using integration by parts. (b) Evaluate f f(x)dx…

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Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vik

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Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: Sketch the region bounded by the graphs of the following functions and find the area of the region.…

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Q: Example 22 Find the eccentricity and directrices of the hyperbola given x? y? 1 9 16 Sketch the…

A: Given: x29-y216=1

Q: Let g(z) = / ft) dt, where f is the function whose graph is shown below. What is the value of g (8)?…

A: We have to find value of g(8)

Q: short

A: Please refer to the image below

Q: 2t +1 lt +8 -dt + 4t +4t 3

A: Let's find.

Q: Use series to evaluate the limit. X-In(1 +x) lim

A: Find your answer below

Q: S etanx sec²x dx

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Q: Find div F and curl F if F(r, y, z) = xz°i+ 2y°x²j+ 6z²yk div F= 2° + 16 y' x + 12 z Y curl F=

A: Given F(x,y,z)=xz6i+2y8x2j+6z2ykTo find div F & curl F:

Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

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Q: 15. Find x² (2x³ + 4)5 dx

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Q: Evaluate the limit using L'Hospital's rule if necessary sin(4x) lim z→0 sin(6x)

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Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: (D2 – 1)y = 2e-*(1+e-2*)-2, %3D

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

A: Given :∫725f(x)dx=c∫27f(x)dx

Q: 1. Let -7 3 -3 2 C = 4 A = B = -3 -3 Determine which (if any) of the following matrices are well…

A: The solution is given in the nwxt step.

Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

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: Determine the radius and interval of convergence of the following power series. The radius of…

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Q: 1- x2 If f(x) = then f'(x) = x² + 1 2/x(x² + 1)³

A: Given : f(x)=xx2+1   To Show: f'(x)=1-x22x(x2+1)3