Let f(x) = 6Va + 1. a. What is the average rate of change of f over the interval from x = 3 to a = 4.5? Preview b. What is the average rate of change of f over the interval from a = 4.5 to x = 6.6? Preview c. f(a) = 92.78 and the average rate of change of f over the interval from a = a to a = a + 220 is 0.164. What is the value of f(a + 220) ? (Hint: think of the average rate of change as a constant rate of change.) f(a + 220) Preview

Q: Find the tangent plane to the equation z 3y cos(5z 6y) at the point (6,5, 15) Question Help: OVideo ...

A:

Q: Need help with part (a). Please explain each step and neatly type up. Thank you :)

A: Please see the below detailed solution.

Q: Find the derivative of the function f(t) = te-t. f'(t) =

A:

Q: 0. If y = Ax) is continuous at x = xo, and z = yo =Axo), prove that z = g[f{x)] is continuous at x=x...

A: Explanation of the answer is as follows

Q: The graph shown below is one period of a function of the form y = a sin(k(x - b)). Determine the fun...

A:

Q: 1. Find the first derivative of the given trigonometric function 1 z = 4cos?. 2

A:

Q: Evaluate the indefinite integral sin t cos tdt 3

A:

Q: 7. Find the Jacobian matrix of the following. a) x= (u+v),y = (u-v).= = 2uvw b) x=r cos 0, y =r sin ...

A:

Q: F i n d   t h e   g e n e r a l   s o l u t i o n . (2x – 3y + 2)dx + (2x – 3y + 1)dy = 0

A: We will use a substitution to solve the equation.

Q: 2. Find the differential. 1 a) z = b) w=2z°ysinx

A:

Q: Consider the function. y = -7 sin-(x) (a) Decompose the function in the form y = f(u) and u = g(x). ...

A: We have a function to find part (a) and (b).

Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 9 s...

A:

Q: 21 The point P in the figure below has y-coordinate 29 y. Find the following. (a) sin t (b) cos t (c...

A: Please see the below picture for detailed solution. 

Q: Find the vertical and horizontal asymptotes of the following: x- (1/x)

A:

Q: Solve Dipferential Eg. 3. dy dx 2xy' e +2xy +Y こ 2

A:

Q: Let R be the region enclosed by the loop of the t², y = t³ – 3t. parametric curve x =

A:

Q: Sx² – 4 if x # -3 f (x) =· {*"_ 7 -2 Evaluate f(4), f(0), f(-3) and f(-2/3) if x = -3'

A: From the given piece wise function, x=4,0,-23≠3 So, the function for x=4,0,-23 is f(x)=x2-4 Therefor...

Q: This is a Partial Differential equations problem. Please provide the answer typed out but if handwri...

A: Solution is given below 

Q: The gradient of f(I, y) = ry at (1, y) = ( – 1, 1) is Question Help: OVideo

A: To find the gradient of f(x,y)=xy  Given (x,y)=(-1,1)

Q: Determine the range of the quadratic function. Give answer as an inequality f(x)=3(x^2 -8x/3) +3

A:

Q: 4 Evaluate sin“ x cos x dx.

A: using integration by substitution

Q: Determine where the function is (a) increasing, (b) decreasing, and (c) where the relative extrema o...

A: Given the functiony=7ex−3e−x

Q: Find the equations of the normal line to the surface z 6z y at the point (1, -1,-6) t+ 6 Submit Ques...

A: To find the equation of normal line to the surface at (1,-1,-6)

Q: Let g(x) = f(t) dt, where f is the function whose graph is shown. y 20아 15 f 10 t 10 15 20 25 30 35 ...

A:

Q: An ellipse has vertices (4, 2) and (4, -4) , and foci (4, 1) and (4, -3). What are the coordinates ...

A: Given, The coordinates of the vertices of the ellipse are   (4, 2) and (4, -4) , and foci (4, 1) and...

Q: Consider the function. y = tan(sec(x)) (a) Decompose the function in the form y = f(u) and u = g(x)....

A:

Q: 5. Prove that if F, G are vector fields on R3, then curl(F + G) = curl(F) + curl(G).

A: Let the vector fields F and G are: F=Fxi+Fyj+FykG=Gxi+Gyj+Gzk Then,  F+G=Fxi+Fyj+Fz+Gxi+Gyj+Gz=Fx+Gx...

Q: Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of...

A: This question is based on application of Derivative.

Q: Find the maximum rate of change of the function f(r, y) 4y² at the point (4,2) Question Help: OVideo...

A:

Q: calculate L4 for f(x)=76 cos(x/2) over [2pi/4, 2pi/2]

A:

Q: Use the polynomial function below to answer the following questions. g(x) = 5x? – 7x + 12 a) Determi...

A: The degree of the polynomial is the highest power of the variable in the polynomial. The leading te...

Q: A 40-ft wide tunnel has the shape of a semiellipse that is 5ft high a distance of 2ft from either en...

A:

Q: . Let p(x) = Ax² + Bx + C. Prove that for any interval [a, b], the value of c guaranteed by the Mean...

A:

Q: J is monotone increasing on an interval and has a jump discon- tinuity at 2o in the interior of the ...

A: Given:  F is a montonic increasing on an interval I and has a jump discontinuity at x0 in the interi...

Q: Find the value of X(0.25) for the initial-value problem dx = xt, x(0) = 2 dt using Euler's method wi...

A:

Q: if 2x^2+3x+xy=2 and y(2)=-6, find y'(2) by implicit differentiation

A: Firstly, Differentiate the given function with respect to 'x' and find y'(x). After that find y'(2).

Q: Acompany produces a special new type of TV. The company has fixed costs of $499,000, and it costs ST...

A: Since you have asked multiple question, we will solve the first question for you. If you want any sp...

Q: 3 5 (c) 4 2 -7

A:

Q: A 23-ft ladder is leaning against a building. If the base of the ladder is 5 ft from the base of the...

A: Since the triangle ABC is right-angled. Consider the length AC is the length of the ladder, BC is th...

Q: 3. Let F be the vector field (ze*z + yz², xz², xe²z + 2xyz) (a) Find the divergence of F. (b) Find t...

A: Answering part b as asked  

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =...

Q: If g(x) = cos(x) then g'(x) = g'(1) = %3D Question Help: D Video MMessage instructor Add Work Submit...

A:

Q: 4.2 Compute the following determinant efficiently: 1 2 -1 0 2 07 2 1 1 1 -2 -1 2 0 0 1 1 122N1

A:

Q: 4 sin x If f(x) then 1 + cos x f'(x) = f'(2) =

A: Topic:- Derivative 

Q: 2x

A: We need to integrate the above given  equation.

Q: -11x Let f(x) = Evaluate f'(x) at x = -T. sin(x) + cos(x) f'(-x) =

A: Here, the given function is: f(x)=-11xsin(x)+cos(x) To find f'(-π). For that first of all to find th...

Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 7 s...

A:

Q: Refer to the figure below. 13 11 20 (a) Find the angle opposite the longest side. (Round your answer...

A: Here is the solution of the given problem.

Q: 5. on the space provided. Vertex Opening Equation Graph 1. 2. y=4-x2 4. 3. y (x+5)2 6. y 1+3(x- 6)²

A:

Q: dy dx (y+1)(x-2)(y-3 (x+1)(v-2)(x-3 ||

A: Here we have to use variable separable to solve the given differential equation,  dydx=y+1x-2y-3x+1y...