4х if х> -1 f(x) 3D { 5 — х2 if b < x<-1 Зх + 7 if x < b

Q: g (x) = sin(x) Compute IT IT + g' + g" 2

A: This question is based on derivative of a function.

Q: An angle's initial ray points in the 12-o'clock direction and the terminal ray rotates CCW. Let θ…

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Q: Consider the expression (3x² + 2/x)10 a) Find a simplified formula for the general term. (separate…

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Q: Solve for the following application of first order differential equations. Show your solutions. 3. A…

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Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: A ball is thrown into the air and its position is given by h(t)=−7t^2+41t+23  where h is the height…

A: Given the position function of the ball is h(t) = −7t2 + 41t + 23

Q: x ys dA X² +1 R.

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Q: 1. 9. 2

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Q: Find the centroid of the region lying between the graphs of the functions y = 11 sin(x) and y = 11…

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Q: Solve through Bernoulli's Equation: * - y = xy O y-l +x – 1 = ce¯* O y + x – 1 = ce"

A: The standard form of Bernoulli's equation is: dydx+Py=Qyn Where; P &amp; Q is the function of x.…

Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of…

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Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

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Q: Solve the following items and show your solutions. a.) Find the general and particular solution of…

A: x dydx+2 y =4x2dydx+2x y =4xComparing with Bernouli's equation;y'+P(x) y = Q(x)P(x)=2x, Q(x)=4x

Q: Find the slope of the line that is tangent to the graph of f (x) 2a-3 at P(3/2, 0) О -3/4 O 2 O (E)…

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Q: Express the limit lim > (7 sin (27) + 6)Az, over [2, 4] as an integral TL 00 1-1 Provide a, b and…

A: Formula :

Q: Use vectors to show whether or not the points form the vertices of a parallelogram. (1, 1, 3), (4,…

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Q: If f(x) and g(x) = In x, then (g o f)(x) =

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Q: Learning Task 4: Given the equation x2 +y² =9. 1. Differentiate using implicit differentiation. 2.…

A: Since, the student has mentioned to solve only part numbers (4) and (5), so we are solving part…

Q: dy Find for the following expressions: dx a) y = x5 In(3x) b) y = 2 cos (+ 2x³ c) 3x2 + 7x + cos (x)…

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Q: Use synthetie division to show that X is of the thiRd - degree polynomial equation , and solution…

A: Given problem:- x3 -3x2 +2=0  And x=1+√3 is one root then using synthetic division factor given…

Q: A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved.…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given:      y=4sin3x      y=4cos3x     x=0, x=π12 Volume of solid of revolution between curves is…

Q: S 3xe*dx

A: Given problem :- ∫ 3xex/2 dx

Q: A restaurant wants to prepare meals for 4 customers. In the restaurant there are only 2 kinds of…

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Q: Write the first three terms of the sequence whose general term is an=n!3n. Provide your answer…

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Q: Use the figure to estimate the limits if they exist. 30+ 20 10 -10 10 20 30 If the limit does not…

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Q: -4x + y = 5 52. 6x - 2y = -9

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Q: 2. Consider the graph shown on the right. a) What is the minimum and the maximum value? b) What is…

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Q: 3 Given y = (1– V2x)°; Find dy/dx O dy :-3(1 – v22)? de O (E) None of the choices O dy 3(1 – V22)°…

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Q: ind cylindrical coordinates of the point with rectangular coordinates (3, –3, –7).

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Q: d. x cosy + y sin x –1 = 0 3 х е. = 2 x y

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Q: The functions f and g are continuous and differentiable with g(x) = f'(x). Selected values of the…

A: Given query is to find the average valu e of function g(x).

Q: Find sin(2x), cos(2x), and tan(2x) using the given information. 7 csc(x) cos(x) < 0 2' -

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Q: 5. * 1 dx х (In x)3 1 + C 2 (In x)² 1 + C 3 (In x)2 A C 1 + C 2 (In x)? B D z+C 3 (In x) O A В E…

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Q: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: Consider the following. u = 5i - j - k, v = -i + 5j + 2k (a) Find the projection of u onto v. (b)…

A: The expression for the vector projection of u onto v is: projvu=u·vv2v And The expression for the…

Q: 1. Evaluate the indefinite integrals: – 2x - | а. 3x*

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Q: Is it log or ln that should be used?

A: You are right. There was a mistake from our end.  Here is the correct explanation: y=x3x Take ln on…

Q: Evaluate the following indefinit 4. Ssin'x cos*x dx

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Q: 1 Use the geometric series 1 >a* for |æ| < 1, to find a power series representation k=0 for the…

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Q: Direction: Find the differential equation of the family of curves described. 3. Find the family of…

A: We are asked to find the family of curves of straight lines with slope and `y` -intercept equal.

Q: Simplify tan(A+ arcsin?). O (2V13)/13 (3 V5)/5 (2 V5)/5

A: Given query is to simplify the expression.

Q: 3 cos(r)ln(1+ a*) + ® 3.8 COS( Evaluate da. 1+el76z 39.9 answer

A: In the given integration we can see that the limit of the integration is from x=3 to x=3  i.e. only…

Q: 4. [Geogebra Question] Let f(x) = (1 – x) In(x²)+3.0225887223. Use Geogebra to find the definite…

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Q: Let there be the random vector Z E Rm Prove that E (||Z||*) = tr(E[ZZ"]) From the expression above,…

A: The answer is in step 2.

Q: 5. The solid below, known as Gabriel's Horn, is generated by rotating the graph of y = ! about the…

A: To find out the volume of Gabriel's Horn.

Q: t? +4r+10 dt 7² + 2r² + 5t

A: I am attaching image so that you understand each and every step.

Q: 3- use Cramer's rule to solve the system 8x1-4x2+3x3=0 X1+5x2-X3=0 -2x1+6x2+X3=0

A: Here we have to use Cramer's rule to solve the system.  8x1-4x2+3x3=0x1+5x2-x3=0-2x1+6x2+x3=0

Q: the length of a child's square-based jewellery box is 5 cm more than its height. the box has the…

A: Topic  = Algebra