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Q: Write a definite integral that represents the area of the region.                               f(y)...

A: Consider the following equation of curve: fy=y-22 Limit is y=0 to y=2.

Q: Find the area of the triangle having the given measurements. C=97°, a 3 meters, b= 8 meters

A: detailed solution is given below

Q: Find all the values of x such that the given series would converge. (x – 2)" 2" n=1 The series is co...

A: Given, ∑n=1∞(x-2)n2n

Q: Explain why the sine or cosine of an acute angle cannot be greater than or equal to 1.

A: In a right angled triangel, hypotenuse is always greater than other sides. And we know, sinθ=perpend...

Q: please show all the work. use integrate by parts

A: It is given that, ∫e2xcos3x dxWe have to evaluate it.  

Q: Approximate the definite integral using the Simpson's Rule with n = 4. (Round your answers to four d...

A: Given, ∫0π2sin(x3)dx Use Simpson's rule with n=4,

Q: Find suitable coefficients (an) so that the resulting power seriessigma anxn has the given propertie...

A: To find: Suitable coefficient an  so that the resulting power series  ∑anxn  has the property: Conve...

Q: Find the indefinite integral and check the result by differentiation                         ∫ 6x2 /...

A: Consider the following integral: ∫6x24x3-93dx Substitute 4x3-9=u→12x2dx=du→6x2dx=12du in the above i...

Q: 10T Use reference angles to evaluate sec 3 Enter the exact answers. For the number 7, either choose ...

A:

Q: Integrals involving hyperbolic functions Determine the indefinite inte- gral fx coth x² dr.

A: Given integral is ∫x coth x2dx  

Q: Express i(1- i)(2-i)(2+6i) in polar form

A:

Q: Determine whether the statement is true or false "The curve given by x = h + a cos θ and y = k + b s...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Find the angle 0, in radians, in the given right triangle. The length of the side adjacent to 0 is 1...

A: Given, The triangle is right angled triangle, so formula of Tan theta can be used.

Q: Write the general forms of the equations of the lines that pass through the point and are (a) parall...

A: the equation of the given line is y=-3. the given point is (-1,0). we have to write the general form...

Q: Factor completely: 81x4 - 16.

A: The expression is 81x4-16.   Use the following identity. A2-B2=A+BA-B   Factorize. 81x4-16=9x22-42=9...

Q: c) Use trigonometric substitution to integrate dx 4-x2

A:

Q: Vector w has initial point (2, −1, 3) and terminal point (−4, 7, 5). Which of the following vectors ...

A: we know that vectorV→ which have initial pointx1,y1,z1 and terminal pointx2,y2,z2 is given by V→=x2-...

Q: Velocity and acceleration from position Consider the following position function.a. Find the velocit...

A: Given, Position function r(t)=13cos2t,12sin2t,5sin2t A)The velocity of object is given by with posit...

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: To evaluate: ∫0π2sin2θ cosθ dθ Solution: Let substitute t=sinθ dtdθ=cosθdt=cosθ dθ Limit will also c...

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then ...

A: Given:∫cscθcscθ-sinθ dθ

Q: Use your result in part (a) to determine if the series is convergent or divergent. Clearly explain y...

A:

Q: If f(x) = In(tanh(2æ)), then f'(x) is %3D Select one: O a. coth(2a)sech (2r) O b. 2 coth(2a)sech (2r...

A: Given: f(x) = ln(tanh(2x)) -------------------------------------------------------------------------...

Q: The temperature of an ingot of silver is60°C above room temperature right now. Twenty minutes ago, i...

A: Given: The temperature of an ingot of silver is 60°C above room temperature. Also, the temperature t...

Q: find an approximate value for square root of 627

A: we have to find an approximate value for square root of 627. that is we have to find an approximate ...

Q: How would you evaluate∫tan10 x sec2 x dx?

A: given ∫tan10 x sec2 x dx

Q: Find the indefinite integral. (Use C for the constant of integration.) sinh(5 - 8x) dx

A:

Q: Please see the attached picture of the Calculus problem. If you could show the detailed work, that w...

A: Given vector field, Fx, y, z=sinyzi+xzcosyzj+xysinyzk Vector field is conservative if Curl F=0 Used ...

Q: Completing the square Evaluate the following integrals.

A: To evaluate ∫dxx2-6x+34

Q: Find the area of the sector of a circle with diameter 28 feet and an angle of radians. Round your an...

A: detailed solution is given below

Q: Find all the values of x such that the given series would converge. * (9x)" 00 Σ n=1 The series is c...

A: Given series,   ∑n=1∞an=∑n=1∞9xnn9

Q: Use a double integral to find the volume V of the solid that is common to the cylinders x² +y = 81 a...

A: If z=f(x,y) and z=g(x,y) are surfaces and f(x,y)>g(x,y) then volume between f(x,y) and g(x,y) is ...

Q: Find the volume of the solid obtained by rotating about the y-axis the region under the curve y 1/(1...

A:

Q: Find the derivative of  f(x) = tan(cos(x^2))

A: f'(x) = d (tan(cos x2)dx  f'(x) = sec2(cos(x2))d cos x2dx               because   d (tan(x))dx = sec...

Q: Calculate the volume of a water cylinder with total height of 10 meters and whosediameter is 400 cen...

A: Height=h=10 metersDiameter=400 centimeters=4 meters⇒radius=r=2 meters    ∵Radius=12·diameter Now vol...

Q: Calculate the iterated integral by reversing the order of integration: (see attached)

A:

Q: Select all the functions that are periodic O tan(x) O sin(r) O csc(r) O sin-'(x)

A: Answer and explanation is given below..

Q: Suppose that A, B, and C are thecorner points of the thin triangular plate of constant density shown...

A: we know that for a triangle medians intersect at center of triangle and centerC of triangle whose ve...

Q: u = a. V =2 1 Suppose is the angle betweenu and V. Then the following holds: If cos e = 0, then a = ...

A: u=2a1,  v=122 Now, cosθ=0⇒θ=π2 Therefore the vectors are perpendicular.  It means their dot product ...

Q: 4. determine the order of the given differential equation; also state whether the equation is linear...

A: d2ydt2+sint+y=sint

Q: Find the explicit formula Doe the general nth term od the geometric sequence described below.  a4=48...

A: