Write clear and detailed solutions for each problem. 1. Determine the amplitude, period, vertical shift, and an equation involving the sine function for the graph shown below. There is no phase shift. f(x) 1- -5 -4 -3 -2 -i 0 i 2 3 4 5 -1- -2- -3 -6+

Q: 3. Find the equation of a curve for which y" = 6x - 4 and which passes through (1,2) and (-2 ,5). 4....

A: 3.y''=6x-4 and which passes through (1,2) and(-2,5).4.f''(x)=12x2+6x-4 and f(0)=4 and f(1)=1.

Q: onsider the ellipse E in the xy-plane defined by the equation ax2 + y2 = 1 where a is positive. (1)...

A:

Q: 1. y'dx- (xy + y² }dy = 0 Let the substitution y=2; y= vx; dy =vdx+ xdv %3=

A: Since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: Use the General Power Rule to find the derivative of the function. g(x) = 4/(6x2 + 5x)9

A:

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

A: use some property of limits.

Q: Suppose h(1) = (f(x) + VI) · g(x), f(4) = 3, g(4) = -1, and f'(4) = gʻ(4) = 5. What is h'(4)? Expres...

A: solution:-Given:h(x)=f(x)+x·g(x)f(4)=3g(4)=-1f'(4)=g'(x)=5

Q: Use differentials to approximate the change in cost corresponding to an increase in sales (or produc...

A: Solution ) c = 0.075x2 + 6x + 2  with dx = 1  differentiate with respect to x  dc/dx = 0.075 × 2 x +...

Q: 2.- In the following problem, use properties of the definite integral, either definitions or theorem...

A: Follow the procedure given below  

Q: What is the differential equation of the family of lines whose sum of the intercepts is fixed as k ?...

A: Given:  What is the differential equation of the family of lines whose sum of the intercepts is fixe...

Q: 8 -5 -8 Factor out (1 + z )° from (256z°+ 150z + 150z - 25z- 25z° + 3 + 3z1

A: Given:    256z-5+150z-4+150z-6-25z-2-25z-8+3+3z-10

Q: Center of Mass: Thin plate (region in the plane). Suppose Ris the region bounded from above by the g...

A:

Q: 0.2 0.4 0.6 0.8 1.0 (sec) s (ft) 0. 0.5 1.5 4.0 6.4 9.6 (a) Find the average velocity over the inter...

A: Given that:                          

Q: Use the Integral Test to determine whether the infinite series is convergent. n=1 Fill in the corres...

A:

Q: (In(x))? 3

A: We have to apply rules of integration to solve the problem

Q: 2) Use the change of variables formula and an appropriate transformation to evaluate fſ, xy dA where...

A:

Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = |F(z – 3i)| wh...

A:

Q: Question 7: Evaluate v² dv (Reimann Method)

A:

Q: Center of Mass: Thin plate (region in the plane). Suppose Ris the region bounded by the graph of f(z...

A: We need to find center of mass.

Q: Find the limit. (If the limit is infinite, enter 'o' or '-co', as appropriate. If the limit does not...

A: Given that: limx→∞(e-x+4cos6x)

Q: Q2: Shear the following object along y-axis, shy = 3 (4,6) 6. 4. 3. (2,3) (4,3) 1 3 5 Q3: A line def...

A: note: as per our company guidelines, we are supposed to answer only one question. kindly post other ...

Q: x3(75 − 14x4)5 dx

A:

Q: The graph of a function f is given. Use the graph to answer the question. Find the numbers, if any, ...

A: The local minima is a point in at which the function has a minimum value in its neighbourhood.  

Q: By using substitution method, evaluate: (a) dx (e3x+x3)3 (In x) dx (b) 4x

A: To evaluate the integral.

Q: An investment firm expects the price of the Campbell’s Soup Company stock to increase via P(t)  =  P...

A:

Q: 2. x*dy +(2.xy – y° )dx = 0 Let the substitution v=2; y=vx; dy= vdx + xdv

A:

Q: Find the limit , if it exists:(Do not use L'Hospital's rule) 16 lim 2→16 16 Note: Give the exact ans...

A:

Q: Find the area between the curve and the x-axis for the function y = x2 +3x between x= -1 and x = 2 a...

A: To

Q: 5 The function f(x, y) = | x' cos is homogenous inx and y of degree

A: Given that: f(x, y)=x2cos2yx-y2+x3y

Q: Determine the parts U Ind du for the following integral XVX-3 dx

A: Given query is to find the integration using substitution.

Q: x^3 + 3x^2 – 1 = 0, [-3, -2] Use the Fixed-point iteration method and Bisection Method  to find solu...

A:

Q: What have you learned in evaluating integrals?

A:

Q: and evaluate the integral that gives the volume of the solid generated by revolving the plane region...

A:

Q: Seax sinh ax dx ах

A: Given integral is  ∫eax·sinhax dx To evaluate the value of given integration, we will use the    sin...

Q: Find the volume generated by revolving the region above the curve y=x3 , under the line y=1, and bet...

A: Figure of y=x3 , y=1 and x=1

Q: Find the derivative of f(x) =-2/- Type your answer without fractional or negative exponents. Use sqr...

A: Let's find. 

Q: Solve the homogenous equation. 2. x*dy+(2.xy– y² kdx = Let the substitution v=: ²; y=x; dy=vdx+ xdv ...

A:

Q: evaluate the indefinite integral / dx. Av7² – 4 xª/x² -

A:

Q: A car is travelling at 72 km/hr. At a certain instant its brakes are applied to produce a constant d...

A:

Q: [ tam2 tam 2 sec 2 Bd ß

A: Given that: ∫5tan2β.etan2βsec22β.dβ

Q: Bottled Water Sales The following chart shows annual per capita sales of bottled water in the United...

A:

Q: f (x) = 2x? + 10, g(x) = 4x + 16

A: Topic:- geometry

Q: Finding the length of a curve. Arc length for y = f(x). Let f(1) be a smooth function over the inter...

A: The given function f(x)=253x32-8 over the interval 3,5

Q: 4922 – 75x – 19 – 4x Find the limit, if it exists: (Do not use L'Hospital's rule) lim x-00 86x + 7 N...

A: Here we have to find the limit.

Q: Please solve and show all work. Thank you!

A: Topic:- geometry

Q: Find the partial fraction decomposition of the function. Write answer in simplest form. 10 b) f(x)= ...

A: Given that: f(x)=10(x-1)(x2+9)

Q: Recall from our lesson that a Non - Homogenous 2nd Order Differential Equation has 2 sides: The Char...

A: Given that, There are two differential equations following, (i). y'' - 3y' - 10y = 5e-2x (ii). y'' +...

Q: Let f(x)=2x2+12, and let   r(x)=sqrt(9x) for x>0. Find a simplified formula for the composite functi...

A:

Q: 2. x'dy+(2xy-y'dr = 0 Let the substitution y=2; y= vx, dy=vdx+ xdv

A: x2dy+2xy-y2dx=0

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic ...

A: We will find the T2(x) and T3(x) for the given function.Below find the solution in the image.

Q: Rewrite the statement in mathematical notation. (Let n be the number of cases of Bangkok flu and t b...

A: Given that - There are currently 200 cases of Bangkok flu, and the number is growing by 20 new cases...