Consider the following curve. y = 3x² - 9x + 1 Find the slope m of the tangent line at the point (4, 13). m = Find an equation of the tangent line to the curve at the point (4, 13). y =

Q: Find the complete solution: (cos2y - 3x²y²)dx + (cos2y — 2xsin2y — 2x³y)dy = 0

A: This is a differential equation of form Mdx+Ndy=0 and if ∂M∂y=∂N∂x.Then solution of the differential…

Q: Use the definition of derivative f'(x) = lim h→0 f(x+h)−f(x)/h to find the derivatives of the…

A:

Q: Find an expression for the inverse of f(x) = e³x+1. f-¹(x) = 4

A: Topic- functions and inverse functions We are given, f(x)=e3x+1 we know that ln(ex)=x

Q: For the function: Show work. 9. a. Find the intervals on which it is increasing and decreasing. b.…

A:

Q: Suppose that f(25) = 10 and ƒ'(25) = −2. Estimate each of the following. 1. f(27) = 2. f(23.5) =

A:

Q: A couple purchasing a home budget $1900 per month for their loan payment. If they have $18,000…

A:

Q: Use the graph to answer # 13-15. 13. Select the function that matches the graph. a. f(x) = |x-31 b.…

A: NOTE: Refresh your page if you can't see any equations. . the absolute value function is in the…

Q: Some banks now have biweekly mortgages (that is, with payments every other week). Compare a 20-year,…

A: let M=monthly mortgage payment P=payment amount r=Interest Rate  n=time T=total interest then…

Q: 1. lim √x+1-2 2²-9

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: A mass on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its…

A: NOTE: Refresh your page if you can't see any equations. . the given position function is  to find…

Q: Solve the differential equation. 2x dy + y dx = 9x5 dx 9 A y 2x11/2+cFx By = 9x5 + c)y= X4+ D)y= 9…

A: Here is the solution:

Q: Is the function below a polynomial? If it is, enter its degree. If not, enter NONE. f(t) = 4/t³ -…

A:

Q: Find an equation of the plane that passes through (8, −2, −3) and is perpendicular to the vector (1,…

A:

Q: Compute the first four derivatives of h(t)=9t2−2et h(t)=9t^2−2e^t. a) h′(t)=   b) h′′(t)=   c)…

A:

Q: Consider the following limit statement: lim (3x-8)= -2 x → 2 Find the corresponding value of ō when…

A: given that limx→2 (3x-8 )=-2ε=0.006we know that f(x)-L<ε  whenever  0<x-a<δ⇔ limx→a f(x)=L

Q: Average Cost for Producing CDs Let the total cost function C(x) be defined as follows. C(x) = 1,000+…

A:

Q: Consider the following function. √√√2²2²-30 (a) Determine an appropriate trigonometric substitution.…

A: The given integral is x2 /sqrt(x2-3).

Q: -8 (†)+($ 4

A: The rows of vectors are added individually.

Q: 4. Find the point midway (-13,-5) and (4.7). 5. The segment joining (6, 5) and (3-7) is divided in…

A: We use section formula:- If a line segment joining by points x1,y1 and x2,y2 divide into m:n…

Q: Determine whether the lines - L₁ :ŕ(t) = ( − 1, 0, − 2)t + (2, − 2, 4) and L2: p(s) = (3, 0, 6)s +…

A:

Q: 2) a) The graphs below are polynomials with leadin Write the completed factor form of each grap 100-…

A: Given graph :

Q: The function f(x) is continuous on the interval [9, 14]. The table below gives some of its values.…

A: f(x) is continuous on 9,14

Q: Solve the differential equation. dy + 5y dx = e-5x dx A) y = 5x + ce-5x B) y = e-5x (x + c) (C)…

A:

Q: Solve the differential equation. y' e³x + 3ye³x = 4x 3x (A) y = 4x²e³x + ce³x B) y = 4x²e-3x + ce-³x…

A:

Q: 1. What is the yield ratio (ratio of servable weight to original weight) for each round? 2. What do…

A: Concept: We have given 1 pound is equal to 16 ounces Converting pound into ounces and ounces into…

Q: Using the properties of combinations of continuous functions, determine the interval(s) over which…

A:

Q: Question The position of an object moving along a straight I after t seconds is modeled by the…

A:

Q: Use logarithm properties to expand the expression log5 O a.) log5 (25x³-y²) O b.) 2+3log5x+7log5y O…

A: Given , log525x3y7

Q: with

A: Please refer to the image below

Q: Find the equations of the tangent lines to the curve y= x^2-2x at its points of intersection with…

A:

Q: Consider the following table. (a) If h(x) = = h'(2) = f(x) g(x) = X 2 LO 5 f(x) f'(x) g(x) g'(x) -3…

A:

Q: 4. The picture shows the graph of cer- tain differentiable function f(x). (a) Find an equation for…

A:

Q: Marginal Profit for Producing Loudspeakers Acrosonic's production department estimates that the…

A:

Q: A tank initially contains [F] m³ of a bleach solution with [G] grams dissolved chlorine. Fresh water…

A:

Q: Simplify (x^2 y^3 z)(x^3 yz^2) and evaluate when x = 1/2  y = 2 and z = 3

A: Topic:- algebra

Q: Please

A:

Q: If the cost function for a commodity is C(x) 13 90 -x³ + 4x² + 4x + 10 dollars find the marginal…

A:

Q: The graph of one complete period of a sine curve is given. y 7 horizontal shift y = 4 (a) Find the…

A:

Q: Use the relationship given in the right triangle and the inverse sine, cosine, and tangent functions…

A:

Q: The area bounded by the curves x = 0, y = e and y = e can be expressed by the integral dx.

A:

Q: Approximate the value below by using a LOCAL LINEAR APPROXIMATIION. DO NOT just simply calculate,…

A:

Q: Find the instantaneous rate of change of f(x) = 3x²-x when x = 2. O a.) 1 b.) 17 O c.) 11 O d.)…

A:

Q: At t=0, a 600 liter tank initially contains 50 grams of salt dissolved in 300 liters of water. Then,…

A:

Q: (d) Graph f(x) = 9x on the window [-9, 9] by [-9, 9]. Do you see why the slope at x = 0 does not…

A: Slope of a function y=f(x) at a point (a,b) is given by   m= dydxx=a

Q: (a) Is it true that cos (2-60°) = 2 cos 60°? Give exact answers in simplest form. cos(2-60°) 00

A:

Q: f(x)= 9x 2 3x² -5x+1

A:

Q: Logarithms turn multiplication into addition. That is, the logarithm of a product of two…

A: We know:- lnmn=lnm+lnn

Q: Find the amplitude, period, and horizontal shift of the function. y = cos(-x) amplitude period…

A: for f(x)= Acos(Bx-C)+Damplitude is |A|period is 2πBHorizontal shift is CB

Q: Sketch 9x2 + 25y2 = 5625 and the line segments connecting (20, 0) and (-20, 0) to (15, 12)

A:

Q: Find the marginal profit function if cost and revenue are P'(x) = given by C(x) = 258 +0.2x and R(x)…

A: