Let f(x) = 25 x The slope of the tangent line to the graph of f(x) at the point (–6, – 25) is The equation of the tangent line to the graph of f(x) at (−6, − 25) is y = mx + b for m= and b = 1

Q: approximate sin 85° Sin a to 4 decimal poths. Compart to ne exact value if you using P(x) of me…

A: Here, to find the Taylor polynomial of the function f(x)=sin x around the point a=π2 which is given…

Q: 4 Water drips into a conical container, which is orientated point downwards, at a rate of 100…

A: This is a problem related to mensuration. Based on the formula for volume of cone and derivative…

Q: Select the conic section represented by the equation. 4x 2 + 3 y 2 - 2 = 0 parabola point ellipse…

A:

Q: Problem 2. Do both parts. 12 4 8 Part (a) Find the sum: + ·+· 3 9 27 81 Part (b) Solve the equation…

A:

Q: gas is escaping a spherical ballon at the rate of 4cm per minute . how fast is the surface area…

A:

Q: An open box of maximum volume is to be made from a square piece of material, s- 12 inches on a side,…

A:

Q: Using the data in the table, approximate g′(3). Using correct units, interpret the meaning of g′(3)…

A: Consider a function y =f(x) .Then f '(x) is the rate of change of y with respect to x.

Q: (a) [1.1] (b) [1.1] (c) [-0.1] (d) [-0.1] (e) [2.99] () [-2,99]

A: We have to find the value

Q: x²+x dx (x²+1)(x+2)

A:

Q: What is the area enclosed by the curve r = 2 cos 30? Answer is in square units. Use two (2) decimal…

A:

Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

A: We have to convert the given equation.

Q: Consider the space curve r(t) = (cost cos 2t, cost sin 2t, sin t). (a) Find r(t).

A:

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A:

Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = , y =…

A:

Q: 1 x + ex 2 g dx

A:

Q: Evaluate the definite integral. 12 dx 25 + 2x 2

A:

Q: 109. f(x)=x* tan x³ -x In (1+x2), then the value of (b) 1 dª f(x) dx 4 at x = 0, is: (d) 15

A:

Q: suppose f(x)= x^3+ax+b where a<0 and has stationary points at (-2,3) find a and b and find position…

A:

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A: Given problem:- A cardboard box manufacturer wishes to make open boxes from rectangular pieces of…

Q: Consider the vectors. (5, -8), (-4,1) (a) Find the dot product of the two vectors. -28 (b) Find the…

A: Given problem:- Consider the vectors.   &lt;5, -8&gt;, &lt;-4,1&gt;   (a) Find the dot product of…

Q: 10. If 3(a, 3, 2)-2(3, b, b) = (-3, 1, -2), determine a and b. Describe the set spanned by the…

A:

Q: Find the first four terms of the binomial series for the given function. (1+5x)1/2 5 125 25 OA. 1-x+…

A: We can find the first four terms as below.

Q: f(Tn) f'(In). For the function f(x) = r- 2x 3. write Newton's formula as n 1 F(In) for solving f() =…

A: See the answer below

Q: 2 Evaluate thefallowing cartesian integrats by - changing theminteequivalent Palar integralse 4- to…

A: Solving

Q: ICLO-3 Use the graph to ist() de.x) dx and S(x) dx in order, from smallest to largest 05 0 0.5 52 25…

A: Here, the curve is above the x-axis for [0,1] and the curve is below the x-axis for [1,2] &amp;…

Q: Find each limit, if it exists. (a) lim + 4 x-00 x - 3 X4 + 4 (b) lim X 00 x -3 + 4 (c) lim X- 00 x3…

A: All the limits are in indeterminate form, just taking common  some power of x from numerator and…

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A:

Q: x2 – 3x – 2 - if x 4 f(x) = /2x + 1

A: To find which discontinuity is at x=4.

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A:

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

A:

Q: The equation of motion of a particle is s = t³ - 27t, where s is measured in meters and t is in…

A:

Q: The eigenvalues of the matrix 139 - 84 240 145 (a) Find an eigenvector corresponding to X₁ = 1 X1 =…

A:

Q: 3. Graph the hyperbola, put the equation into standard form and identify the asymptotes, vertices,…

A: The given hyperbola equation,      9x2-4y2-36x+8y-4=0

Q: Solve f(x) Sin e* (12 intervals) Using Trapezoidal Rule(Numerical Methods) ['re f(x) dx

A: Solve the following

Q: A rectangular solid (with a square base) has a surface area of 37.5 square centimeters. Find the…

A: We are given a rectangular solid with square base whose surface area is 37.5cm2. We have to find…

Q: Find dy/dx: solution in handwritten 1. y = 5* (** + dx VE х4 3 -x²,

A: Using leibnitz rule for integral.

Q: The non-homogenous solution of the following equation by using variation of parameter method y" +y =…

A:

Q: g expressions a. lim (2z - 1)(2-1)

A: Given : apply chain rule    find limit of about separately

Q: Find all zeroes of f(x) = 4x² - A) --/1/201 B) 1 3x² - x. Check all that apply.

A: f(x)=4x4-3x2-xZeros:4x4-3x2-x=0x4x3-3x-1=0x4x3-4x2+4x2-4x+x-1=0x(4x2(x-1)+4x(x-1)+1(x-1))=0x(x-1)(4x…

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A:

Q: Let C₁ be the curve with parametric equations I= cost, y = sint -t, where t € [0, 1]. (a) Find the…

A:

Q: Solve the following: 1. Create a table, a verbal description, and a piecewise function to represent…

A:

Q: y² − 5y = x³ - e² +c where c is the of integration. Setting x= we have . Thus, we have y — 5y — ( —…

A: This is a problem related to integration. Based on the general formula we will answer the question.

Q: Use Newton's method to approximate a root of the equation z + c + 3 - 0 as follows. Let I, = -1 be…

A: Let's find.

Q: For what values of x does the series converge conditionally? 5x Σ n! n=1 1 O A. x= -7 5 OB. X=0 1…

A:

Q: Below is a graph of f(x) = sin x. Find the total area trapped between the curve f(x), the x-axis,…

A: Follow the procedure given below.

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: consider the polar equation defined by r = 5 cos(2 sin 8), where s0< 2n. Determine the missing…

A: as points are already find π6,2.70    π3,-0.80    π2,-2.08  3π4,0.77                      π,5…

Q: Problem 3. Solve 2+2 =10 4* +4 = 68

A: To solve the following system of equations.2x+2y=104x+4y=68