21-24 Find an equation of the tangent line to the curve at the given point. 21. y sin x + cos x. (0, 1) 22. y (1+ x) cos 1, (0, 1) 23. v COS A sin x, (7,1) 24. y + tan x. (. )

Q: Show that V is not a subspace of R³: V is the set of all (x, y, z) such that x + y + z = 3

A: We need to prove that V is not a subspace of R3  .Below find the solution in the image.

Q: Assume cos(t) = - where <t <a. Compute the following %3D cos(-t) = sin(t) = sin(-t) =U sin(-t) + cos...

A: topic - trigonometric ratios sin(-x)=-sin(x) cos(-x)=cos(x) sin2(x)+cox2(x)=1

Q: (g) sin vt dt.

A: Intigrating the given equation. 

Q: dy (2a³ – 3x²y + y³) 23 – 6x²y + 3ry? dx %3D

A: This question is based on solution of homogeneous differential equation.

Q: The velocity of a moving particle at any time t is given by expression 12t2 + 10t +7. If when t = 1,...

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Q: Evaluate the double integral // (3r - 7y)dA, where D is the domain bounded inside the tangle with ve...

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Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12, -...

A: Area of the Region bounded by the curves :If f(x) and g(x) are two continuous function on a,b and f(...

Q: In Exercises 11-18: (a) Find the domain D of the given function. (b) State whether D is an open or c...

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Q: If  h(x) =    5 + 4f(x),  where  f(4) = 5 and f '(4) = 2,  find  h'(4).

A: Solution: Consider the function h(x)=5 +4f(x) f(4) = 5 and f '(4) = 2 (Given)  

Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid generate...

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Q: x²dx x3+ 4

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Q: Calculate the improper integral if it converges, or show that it diverges. 1 dx -

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Q: S(x) 2 -1 2 3

A: The objective is to find f(-4).

Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the p...

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: Series  convergence and divergence 

Q: The temperature at a point (x,y,z)(x,y,z) is given by T(x,y,z)= 1200e^(−x^(2) − 2y^(2) - z^(2)) whe...

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Q: 9. . sinh 3x dp- 1+cos 3x 2x+9 10. S x² +6x-4

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Q: 6. A water tank is shaped like a cone with the apex point at the bottom, where the cone has radius 5...

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Q: Sec o

A: The solution is given in the next step.

Q: If y = x - 4x and x = V2r + 1, find dy/dt when t = 1= V2.

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Q: 9-30 Determine whether the series is convergent or divergent. 20. S. f it is convergent, find its su...

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Q: x +1 if r -1 Determine if lim f(x) exists. 2-1

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Q: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O 1...

A: Given query is to find the area of parallelogram.

Q: 1 Let f(x) = and calculate %3D x(In(x)) S(x) dx by using integration by substitution. What was your ...

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Q: how to solve cos(arcsin[3/5])

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Q: - ydx + x(Inx – Iny - 1) dy = 0, when x = 1, y = e %3D

A: Let's find. 

Q: 10) Find lim [ g (x-2) / f(x) ] = _ A) 3/ 7 B) 1 C) 7 D) 7/ 3 lim g(8x-f(x+2)) = X 1 11) Find A) 1 B...

A: We have to find the value of the limit                                  limx→3g(x-2)/f(x)       and ...

Q: Solve in linear equation or bernoulli (2x+3)y'= y+y²(2x+3)^½

A: 2x+3dydx =y+y22x+312

Q: LU Factorization Method Example 2 Use Cholesky's LU factorization method to solve the system 16х, — ...

A: Given: Matrix is given

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A:

Q: Evaluate the integrals C f (z) dz, where C is the unit circle centered at the origin and f (z) is g...

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: The distance, in feet, a moving object has traveled after t seconds is given by 3t/(4 + t). Find the...

A: We can find the required acceleration as below.

Q: 1. A girl has 6 bags, 11 dresses and 7 pairs of shoes. On how many different ways can she dress up?

A: NOTE: As per our guidelines, I have solved the first problem in the picture. If you want the answer ...

Q: For the given vector function below, find the equation of the plane that contains the osculating cir...

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Q: Express the following functions in terms of function f where y=f(x). Professor Lapan's Helpful Hint...

A: We can solve both the part as below as per the instructions of Professor Lapan's Helpful Hint:.

Q: 32xdx

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Q: From a point 56 feet above the ground, a stone is thrown vertically downward and hits the ground at ...

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Q: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of...

A: The given function is: f(x,y)=y+sinxyGiven point is:  P=(0, 3)

Q: Suppose that in 1662, a man bought a diamond for $34. Suppose that the man had instead put the $34 i...

A: The continuous compounding formula is P(t)=P(0)ertwhere P(0)= the initial amountr = the rate of inte...

Q: 구 -8 -6 -5 -4 -3 4 6 -2 -4 -6 -7 -8- lim f(x) = Enter the limit. If the limit is o, enter oo. If the...

A: We have to find limit.  

Q: Find the six trigonometric function values of the specified angle. 24

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Q: T/2 cos t dt 1 + sin²t

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Q: 35-40 Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the ...

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Q: Ek=1(-1)k-1_7 9k-1 Determine whether the series converges and if so, find its sum. O 1/2 63/8 63/10 ...

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Q: Let f(x, y) = 6x – 2ry and the point M(5, 9). Among all unit directions, there is a unit direction (...

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Q: Find the average velocity over the interval [1,4] Find the average velocity over the interval [1,1 +...

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Q: Let f(x) = and calculate V15 x+1 f(x) dx by using integration by substitution. What was your substit...

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Q: Find the equation of the plane that contains the point (3, 2, 3) and the line  x = -4 +4t, y = -3t,...

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Q: Test each of the following series for convergence by either the Comparison Test or the Limit Compari...

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