Find the equation for (a) the tangent plane and (b) the normal line at the point Po(2,0,2) on the surface 2z - x² = 0. (a) Using a coefficient of 2 for x, the equation for the tangent plane is (b) Find the equations for the normal line. Let x = 2 - 4t. y=0, z=0 (Type expressions using t as the variable.) x=₁ y= X ...

Q: Tutorial Exercise Evaluate the integral. J 65 (x - 1)(x² +64) Step 1 The given function lu dx 65…

A: Use the partial fraction

Q: Assume that the recursively defined sequence converges and find its limit. a₁ = -20, an+1 = 20+ an…

A:

Q: Use partial fractions to evaluate the integral 2 1² 2²-2-3 de dx 2x 0

A:

Q: Write a in the form a = a-T +aNN at the given value of t without finding T and N r(t) = (-2t+4)i +…

A:

Q: Define f(0,0) in a way that extends f to be continuous at the origin. 14x²-x²y² +14y² x² + y² - In…

A:

Q: Find an equation in​ slope-intercept form for the line. Through ​(4​,4​) and ​(1​,6​)

A:

Q: Find the critical points of the function f(x, y) = x² + y² + 8x − 4y + 4.

A:

Q: Q3// The curves y = ax² + bx+c and y = cx-x² have a common tangent line at the pint (1.0), Find a,…

A:

Q: lim x 3 x² - 2x - 3 T

A:

Q: What are the domain, range, and period of the function f(0) = 2cse(0 + 1)₂

A:

Q: Use the parameter to write each rectangular equation as a pair of parametric equations. State any…

A: The parameter is

Q: n class I gave a general formula for derivative of an exponential function f(x) = a ^ u(x) ; where…

A: The first part of the derivative formula,  represents the natural logarithm of the base of the…

Q: Consider the following. f(x, y) = 4y y y = 3x-x² D 3x - x² (³x-x² Jx y=x (a) Express the double…

A: f(x,y)= 4yWe have to find double integral over given shaded region

Q: Use integration to find f(4) if d = 2x² and f(1) = 6.

A:

Q: Consider the function (a) Find f(-5, 4). z = f(-5, 4) = -1575 z = f(x, y) = = = x² + 5xy³. (b) Find…

A: Given :z=f(x,y)=x2+5xy3

Q: 4) More Complex Differentiation: Differentiate and simplify the following functions a) g(x)= rcosx…

A:

Q: What is the total change of f(x) between x = 0 and x = 4, when df = sin(2x) ? O 0.573 0.989 O 1.146…

A: If we are given f'(x) and interval from x=a to x=b then the total change is given by the…

Q: I sin sin(ln(x)) dx

A:

Q: Given = and ủ= , find 6 – u. 6q u = .

A:

Q: x Q2// Find the second derivative of y = (x³ +) 3 x

A:

Q: A can is filling with water at a rate of r(t) = t² cm³/sec. If the can was empty at t = 0, what…

A: We have,  r(t) = t2 Can was empty at t = 0Amount of water t = 4

Q: 4. Determine the 75th derivative of each of the following functions. b) f(x)= 3 cos 2x

A: We know that the derivative of cos(ax )is -a*sinx(ax)

Q: Upload a picture of your full solution in one file and attach it to this question. Determine the…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Evaluate the sum 1 Σ² n! n=0 1 + (-1)^²+¹ + (-2)' (−1)n+1 n 2n+1

A:

Q: The graph shown below is f(x)=√x+1.If g(x) = f(t)dt, find g '(3). 5 4 3 2 X 5 4 3 2 1 1 2 3 4 5 कृ…

A:

Q: 7-52 Find the derivative of the function. 7. f(x) = (2x³ - 5x² + 4)5 9. f(x) = √√√5x + 1 8. f(x) =…

A:

Q: If an object's position over time is given by the function d(t) = (t² + 2)e on what interval is the…

A:

Q: Calculate the double integral. | [₂₁ (2y + xy²2) dA, R = {(x, y) 10≤x≤2,15ys2} R

A:

Q: dw Evaluate at (u,v)=(5,1) for the function w(x,y) = xy-y²; x = u-v, y= uv. ди OA. -1 OB. 9 OC. 4 O…

A: Put

Q: Determine the order, n, of the differential equation y" + 4y'y=-3x³. n=

A: y'''+4y''y'=-3x^2

Q: y = x² - ²₁ (-2,5)

A: Derivative by defination rules

Q: Let f(x)=√√9x-5, g(x)=x²-49, and h(x): (fh)(x) 1 X-7 Fi

A:

Q: A region bounded by f(y) = √y, y = 4, and x = 0 is shown. What is the volume of the solid formed by…

A:

Q: Assume the world population will continue to grow exponentially with a growth constant k = 0.0132…

A:

Q: Find ofldx and of/dy. f(x,y) = 4x4y af дх of ду || ||

A:

Q: Use the Laws of logarithms to rewrite the expression log: (2¹4 14 y13 in a form with no logarithm of…

A: Logarithmic Formula

Q: f(x) = ln(x - 2

A:

Q: . Consider a parallelogram generated by the vectors (1, y, -2) and (3, 0, 1). For what value(s) of y…

A:

Q: lim Ax-o+ 8 00 x + 4x Ax 1 8 X

A: We need to evaluate the following limit

Q: Let Σan (x+3)" n=0 denote the Taylor Series of 21 at the point x = −3. 2-x Then a5 =

A:

Q: What is the average value of f(x), between x = 0 and x = 5 for f(x) = 2 + cos(3x)?

A:

Q: (a) ² 2x − 3x + 1 dx - (b) / 1 x² + √x X (c) √ ₁ 13/2 (2t - Vt) dt. S (8) [² (22) dx (2z − 1)(z + 3)…

A:

Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) y 4 2 -2 (a) lim…

A:

Q: Integrate the function f over the given region. 1 f(x,y) = over the square 6 ≤x≤ 10, 6≤ y ≤ 10 xy

A:

Q: If f f(x) dx = a + 3b, then f(f(x) + 6) dx = O 9b-6a O 9b-7a O 9b-5a O6b-6a O a + 3b +6

A:

Q: Find the point on the curve r(t) = (5 sin t)i + (-5 cost)j-12tk at a distance 13 units along the…

A: Given : curve To find : Point on the curve r(t) at the distance 13 from the given point along the…

Q: 1-x² Find lim 18² 8x² + 5° X f(x) 10 100 1000

A: To determine the limit.

Q: An object moves along a line, where its velocity function is as described by the graph below. What…

A:

Q: Which integral would represent the area shown below? The function is f(x) = 2x + 2. 8 6 00 st 4 2…

A:

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

A: