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Q: 2. Determine the slope of the tangent line to the curve f (x) = sin (x)cos (x) at the point where x…

A: Slope, m = d[f(x)]/dx

Q: Evaluate the following definite integrals. Show your solut 1. S eva -dx 2. So sin³ Od0

A:

Q: Find the gradient of the function at the given point. In(x² – y) – 6, (2, 3) z = Vz(2, 3) =

A:

Q: 2²dx Evaluate: 4 – x2 - A f (x) = 4 sin (5) + xV4- a2 +C 2 2 sin- () – xv4 – x² +C В f (x) = 2 ©…

A:

Q: A region bounded by f(x) = 2x-2, y = 1, y = 4, and x = 1 is shown below. Find the volume of the…

A: A region bounded by fx=2x-2, y=1, y=4, and x=1 is shown below.To find the volume of the solid formed…

Q: A region bounded by f(x) = x², y 0, and x = 4 is shown below. Find the volume of the solid formed by…

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Q: 9.There is no function f(x) such that S f(x) dx = f(x) +C. O A. True O B. False 10.lf the integrand…

A: yhi

Q: 1. A biker is 50 meters away from a pole. The biker starts to ride south parallel to the pole at a…

A: Solution is given below:

Q: y' + p(x)y = q(x), p(x), q(x) E C(I)

A: We have to find the general solution of differenrial equation

Q: The particular solution of y(x+ y)dx + (x +2y- 1)dy=0; y(0) =2 by NEDE is A x(x+y-1) = 4e* x(x+y-1)…

A:

Q: 2. Given the function -a Show that

A: Note :-  Since you have asked multiple question As per our policy, we will solve the first question…

Q: -1/2 p. Find the coefficient of x" in the expansion of (1– 4x)2.

A:

Q: Use the Root test to determine whether each of the following series conve n" (5n - Зп3 a) 231+2n b)…

A: We can solve the given problem as follows:

Q: If x =0.42 and y = 0.14, then value of C in the antiderivative of F(x) = ACOS (A) V1-x2 is (use…

A: Given,            The antiderivative of Fx=xcos-1x1-x2 and x=0.42 and y=0.14.To find : The value of…

Q: 1. A biker is 50 meters away from a pole. The biker starts to ride south parallel to the pole at a…

A:

Q: Which of the following is true? (A All for the above ® Stan (x)sec®(x)dx = tan (x), tan?(x) ,…

A: We have to evaluate the following integrals.

Q: 4. Given the graph of f(x) below, sketch the graph of f'(x) and explain how you arrived at your…

A: The graph is drawn by free hand.

Q: Given a function f(x,y) = x* + 2y + 8xy – 7 The critical points of f(x,y) occur at the points P(0 ,…

A: A point (a,b) is said to be a saddle point of f(x,y) if at (a,b)(fxxfyy)-(fxy)²<0 A point (a,b)…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: f) 3rd derivative of y : sin 3x g) Find if yVx – 8 = xy +2. if yvx – 8 = xy + 2. dx

A: Note: As in questions d and e no instruction is given solved f and g for you.

Q: dæ Evaluate: æ/9x² + 4 9x2 + 4+ 2 + C V A f (x) = -4 ln 3.x f (x) = -2 ln V9x2 + 4 + 2 + C None of…

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Q: The integral expression Xsin (2x)dx can be evaluated using integration by parts of the form Sudv=…

A: Here, the given integral is: ∫xsin2(2x) dx

Q: Find the exact real solutions of the following equations. (a) (2 + 1)(3" + 1) = 6" – 4 (b) 3+1 = 52…

A: Let's find.

Q: Use implicit differentiation to find y′ for the equation below and then evaluate y′ at the indicated…

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Q: Given: (x - 2) - (y- 1) 1, identify the center, vertices, and foci. 4. 5

A: Hyperbola

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ - y, P(6,…

A: As we know that; The expression for the directional derivative of the function f in the direction of…

Q: C. Find the derivative of each function. x' - 2x 3. h(x) = 4. F(x)=sin x- cos x- tan x tan x D.…

A: Follow next step

Q: Which of the following is true? @Stan (x)sec (x)dx = sec (x) 2sec7(x), sec (x) + C 6. 7 O…

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Q: 6 Evaluate the fallowing integral.

A: Given,            ∫2cos4xdx

Q: Vn3 + n2 + 1 Determine whether the series converges or diverges. E1 n2 -n+3

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: Given; y=4x2, y=0, x=4   Now find the point of intersection between the curve y=4x2 and the line…

Q: Would it be absolutely convergent or conditionally convergent?

A: Let, for the given series the nth term is an=-1nn15+1n23+3.   Using the ratio test of the absolute…

Q: 21.Which of the following is a particular solution to the differential equation when x = e and y =…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the indefinite integral as a power series. t dt 1 - 7 C + n = 0 What is the radius of…

A:

Q: how would you find the x-values that the function f(x) = 2e^x - 6x have horizontal tangent lines? I…

A: The given function fx=2ex-6x

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A:

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: what are 7 and 8 in standard hyperbola equation? 7) The foci are (-8, 2) and (2, 2). Vertex at (1,…

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Q: dx J x3 – 2x² + 9 – 18

A: Given problem:-

Q: Consider the words u = a?ba b² and v = bab?. Find: (а) (6) uv (b)

A:

Q: ind the definite integcal uoing any method. 3/2 x13-2xdx

A: Follow next step

Q: ​Recently, a certain bank offered a 10​-year CD that earns 2.48​% compounded continuously.   Use the…

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Q: y2-25 -dy is 5 tane - 50 +C, The result of the integral in 0 given A True B False

A: To determine whether the given statement is true or false.

Q: *Sketch all appropriate regions or solids.* Evaluate the integral by using a Jacobian "…

A:

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 2 %3D y + 5 =…

A: The given question has been solved in detail.

Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: Here, the given function is: f(x)=9-x2, a=1

Q: The rabbit population at the city park increases by 4% per year. If there are intially 390 rabbits…

A: Given query is to find the population of the rabit after 18 years.

Q: S¥×(2x³ + 1)dx 3,

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Q: Find the general solution using separationof variables y = re" y = 5ry – 2r Solve r dy = y +1 and…

A:

Q: 1 Using the power series representation 5n with interval of convergence rE (-1,1), 1– 25 determine a…

A: