Find the average rate of change of f(x) = x² - 1 on the interval [–1,0.4]. Give your answer in decimal form. Hint: You can use the applet to do the calculations for you.

Q: A closed rectangular box is to have a square base and a volume of 40 ft3. y Letting x denote the len...

A:

Q: 4. Determine the phase shift and the vertical displacement with respect to y = sin x for each functi...

A: Given problem:-

Q: 7 Compute the exact value of cos (금) Suppose that - is an angle in quadrant 2 and that cos y = 25 co...

A:

Q: For the function below, find (A) f'(x), (B) the partition numbers for f', (C) the critical numbers o...

A: Given query is to find derivative and critical point.

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 8. (5- |x – 5|) dx

A:

Q: Evaluate the triple integral of (1 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 4, ...

A:

Q: Consider the function 1 1- x4 Write a partial sum for the power series which represents this functio...

A: Consider the function

Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given 

Q: y ev = z - 1: y (2) = 0 O = In(z² – 2x + 1) O = In(z? – 2z) + C O = In(z² - +1) O = In(z² – 2z)

A: The differential equation is given by yy'ey2 = x-1 The initial condition is given by y2 = 0 To evalu...

Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The...

A: To find the length and width of the rectangle that has perimeter of 32 with maximum possible area. L...

Q: The population of a country was 5.397 million in 1990. The approximate growth rate of the country's ...

A:

Q: nt Use the model A=Pe" or where A is the future value of P dollars invested at interest rate r conti...

A: Given A=P(1+rn)nt

Q: WeXg+x*g²_x*y% show that wxy=Wyx fnd wiy if waflusu),u=メー 2wefluV)u=メーツ V=xy Express the answer inte...

A: As per our guidelines, I can answer maximum one question. Since you have asked for multiple question...

Q: dy IfY then dz impossible to calculate In(x) II CO

A: As you have asked for the solution of question number 8 only. So I am solving that only. Thank you. ...

Q: 8. 1 Vn(1+vn)

A:

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

A:

Q: The height (in feet) of a rocket launched from the ground is given by the function ft) = -162 + 160t...

A: The given function is  f(t)=-16t2+160t. 

Q: Find the antiderivative of the function f(x) = x*. That is, find a function F(x) for which F' (x) = ...

A:

Q: Given u(x, t) = t-²e¯, 2 , compute:

A: We can find the required answer as below.

Q: 3. - +- 9 + - 8 10 7 9 +

A:

Q: Find dy/dx of the function below. 2x³ + e^(2y) = cos3y

A: 2x3+e2y=cos(3y)Differentiate with respect to x6x2+2e2ydydx=-3sin(3y)dydx2e2ydydx+3sin(3y)dydx=-6x2(2...

Q: Determine whether the two functions are inverses. -5 -5-2x w (x) = and z (x) x+2 dz(x) = O The two f...

A: Given: w(x)=-5/(x+2) and z(x)=(-5-2x) /x. 

Q: Find f such that f'(x)= 7x +7x-2 and f(0)= 8.

A:

Q: Determine the intervals of concavity for the graph of the function f(x)= xe^x. ( Enter your answer u...

A: The graph is shown below::

Q: 13. Let a be a constant. State the formula for the nth-degree Taylor polynomial of a continuous func...

A: Let a be a constant. We have to state the formula for the nth-degree Taylor polynomial of a continuo...

Q: Find the critical numbers and absolute extrema for y on the interval [0.5, 2]. Type DNE if an answer...

A:

Q: d 3) (2a)* = (Derivative of an exponential %3D function)

A:

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A: Here we have to find the volume generated by rotating the region bounded by the given curve about y=...

Q: If 4x²-2y²=9, then find dy/dx.

A: Using defination of differentiate

Q: In each equation in Column A, find . Match the equation with its corresponding Column B. Write the l...

A: Since the student has posted multiple questions and has mentioned to solve multiple questions (quest...

Q: Test the series for convergence or divergence. 1 4. In 3 1 + In 4 1 1 + In 6 In 5 In 7

A:

Q: Use the Geometric Series Test to show that 0.3+0.03+0.003+… converges.

A:

Q: Consider the differential equation y" – 6y' + 13y = e3r By using an appropriate substitution, give a...

A:

Q: 2. An jet travels horizontally at a speed of 500mph at an altitude of 3 miles above the ground. A vi...

A: We need to find rate of change of angle of elevation.

Q: A 5-gallon bucket is full of pure water. Suppose we begin dumping salt into the bucket at a rate of ...

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

Q: 7 f (x) = VE .A is the point (4, 2). Which one of these is an equation of the tangent through point ...

A:

Q: x = 0, y= 1, y = e4 %3D x =-,

A:

Q: 9. The velocity, in kilometers per hour, of a car as it beings to slow down is given by the equation...

A:

Q: find the general solution of the differential equation. y'+2y = xe-2x,    y(1)=0

A:

Q: Find the area of the surface generated by -y -y + e 2 revolving the curve x = in the interval In 2 O...

A:

Q: 4. y = 5 cos 4x, 3rd derivative 5. y = 3 tan 3x, 2nd derivative %3D 5. y = 6 csc x, 2nd derivative

A:

Q: Antiderivative of a Function 12. S(t - 4)² dt

A:

Q: 1. Which of the following are trigonometric identities? Select all that apply sin e tan 8 = cos e co...

A: Find your answer below 

Q: Evaluate lim, 0 (1 - )2". (Hint: take log) 6.5 O 1 O 2 O e?

A:

Q: ° (24 -2x + 2) I-4

A:

Q: logarithm

A: We will expand the logarithms. 

Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must c...

A: topic- application of derivatives

Q: • For numbers 5-10, find the derivative of a given functions. TO 1. lim f(x) = -1 ffx) 3 2 2. lim f(...

A:

Q: Use the Ratio Test to determine whether the series is convergent or divergent. (2n)! 16. У (n!)? 00 ...

A:

Q: 11* Consider the series ak (k + 9) - 62k+1" k=1 a) What is ak+ 1? ak+1 aktl ? b) What is ak a-1/a ak...

A: