Area Between Two Regions Name: (a,h) (0, 0) (b,0) Use integration to determine the area of the triangle.

Q: Evaluate the definite integral. e12' i + e¯*j+tk )dt e12 – 1 1 (e- – 1) + 12 O el2 – 1 e12 -i - (e-…

A: Integral

Q: a b c Given det d e f = 5, find the following determinants. h i a b det d. e f -3g -3h -3i a b det…

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Q: Evaluate the definite integral. i+e'j+t k )dt ell (e-l – 1) + (ell – 1) i – (e-1 – 1) j +, k 11 ell…

A: Given: I=∫01e11t i+e-t j+t kdt   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: 2- Sinx-y cos?x =.

A:

Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

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: xー1 dx (x+1) (x-3)5

A: Use substitution method for solving the  integral.

Q: Evaluate the definite integral. ell! i + e¯'j + t k )dt O ell – 1 (e-1 – 1) - (ell – 1) i – (e-1 –…

A: The given integral is: I=∫01e11ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: 8 Evelluate the double integral: + 3x) 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: 3 roblem 4. The third term of a geometric sequence is 9, and the common ratio is Find the fifth…

A: Given problem:- The third term of a geometric sequence is 9, and the common ratio is 3/2   Find the…

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: 1. Find fa(x, y) and fy(x, y) given f(x, y) = (csc y) Arcsin(r2).

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Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula k(t) to find k(t). 13 r(t) = 10 cos(7t)i+ 10 sin(7t)j+…

A: Given; r(t)=10cos(7t)i+10sin(10t)j+3tk

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 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: d d Calculate ri(t) · r2(t)] and dt x r2(t)] first by differentiating dt the product directly and…

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Q: Find the equation of each normal of the function f(x) = 1/3x^3 + x^2 + x - 1/3 which is parallel to…

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

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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: Sx² sinh xdx

A:

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: Question 5 Consider the exact first order diff. equ: M(x, y) = 2.xy –3x? N(x, y) = x² - 2y (I):…

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Q: Find r'(t). r(t) = (tan(10t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k.…

A: Given problem :- r(t) =(tan-1(10t)) i+t cos(t) j-√tk Find:- r'(t)

Q: Find all the relative extrema and saddle points, if any, of the given function below: f(x, y) = In(x…

A: To find all the relative extrema and saddle points, if any, of the given function below:fx,…

Q: Consider the exact first order diff. equ: |M(x,y) = 2.xy- 3.x? N(x, y) = x² - 2y (I): (2xy - 3x )dx…

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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: 1. 3 de

A: Given integral,         ∫3 dx

Q: Use the Taylor series for f(x) = Vx, centered at a = 16, to approximate the numerical value of v17.…

A: This question can be solved using the concept of Taylor series centered at a.

Q: Evaluate the definite integral. 12t dt O el2 – 1 (e-) - 1) + 2 – 1 i - (e" - 1) j +k 12 O el2 12 O…

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Q: Use the formula r(t) = |r(t) × r"(t)|l| ||r(t)||³ to find k(t). %3D r(t) = t’i + t3j K(t)

A: r(t)=t^2i+t^(13)j r'(t)=d(t^2i+t^(13)j)dt=2ti+13t^12j r''(t)=d(r'(t))dt=2(1)i+13×(12t^11)j…

Q: Q2) Find the integral of: f*,6 tan*x dx

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Q: dx sinxtanx

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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

Q: 15 dy dt 2-

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Q: 1 3. Savads 4Vūdu 4.

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Q: In a

A: We have to find given indefinite integral.

Q: ay dy

A:

Q: Evaluate the definite integral. + ej+ dt - 1) i - (e" - 1) j +k O e? i+ (e-1-1) j+국k 2.

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Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x<1

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: Q2: Solve the following integrals:- (1) fx² sin x dx (2) f dx 4x2- xp: (3)f x sin(x + 1)dx

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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: Q2/A) Find the particular solution for the following D.E., the boundary condition is (y-0@x

A: The given equation is dy=ex-ydx.

Q: Find div F and curl F if F(r,y, z) = 1°i – 7j + yzk. div F= curl F=

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Q: 5. Consider the region R in the plane enclosed by x-0, y=1 and y = x a. Draw the region b. Use…

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Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B

Q: 5x3+4x2-5 dx

A: Use power rule integration technique

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 16 r(t)

A: The given plane curve is   x2+y2 =16.  We have to represent the curve by a vector valued function…

Q: Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2).…

A: Solving