Calculate the linearization L of f(x) = at x=1. Express your answer in terms of e and x. L(x)=

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The answers are as follows: (a) The vector equation of the plane is r.(−9,15,10)=−23. (b) The…

Q: Use implicit differentiation to find y' for 5x³y² + In (xy²) = 5 and then compute y' at (1, −1).…

A: Answer ::The final answer is 1211​Explanation:sol) Hence,The final answer is1211​

Q: how did we find 100/3

A:

Q: 7) Find the derivative of x(x) = (2x+3)³ (2x+3)+2x+4 X + √ 7

A: Given that, we have to find the derivative of y(x).

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) 1-8 Inx;…

A: The objective of this question is to find the equation of the tangent line to the graph of the…

Q: Question 9: Using the fact that i²= -1 and the identities: and cos(x)=(-1)" x2n (2n)!' n=0 x2n+1…

A: Given that To prove

Q: nd the maximum rate of change of f(s, t) = test at the point (0, -3).

A:

Q: 3x3 +5y3 lim (x,y)-(0,0) x² + y²

A: To find the following limit.

Q: What is the rate of depreciation (in dollars per year) after 5 years? The salvage value S (in…

A: To find the rate of depreciation after 5 years, we need to calculate the difference between the…

Q: Express the given rational function as a sum or difference of simpler rational functions

A: The required answer is given below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: A. Find the equations of the intersection line between the planes 3xyz2 and x-y+2z = 3

A:

Q: Hello  I got this answer, but part of the explanation was cut of.  could you help with the missing…

A: Certainly, I can help you with the missing parts of the explanation, and explain how z = u and x = u…

Q: Find a set of parametric equations for the rectangular equation y=4x-4 that satisfies the condition…

A:

Q: d 3 Evaluate dx √√In(6 - x²) at x = 1.

A: −15ln(5)32​2​Explanation:

Q: In (x + √√x². Find the first partial derivatives of the function f(x, y) = ln(x+ 1. fx(-3,4)= 2. fx…

A:

Q: +0+x (4) lim xx

A:

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A:

Q: Find the equation of the tangent plane to the surfaceln(x3 + y3 + z3) = x2z + 1at the point (1, 1,…

A: The objective of this question is to find the equation of the tangent plane to the given surface at…

Q: Given the graph of f, find any values of x at which f' is not defined. Q 2 G OA x=-2,2 OB. x=2 O c.…

A: The derivative of the function is undefined when:The function has a vertical asymptote.The function…

Q: John is floating on a tube in a wave tank. At t 1 second, John goes over a wave at a maximum height…

A: We need to solve the sinsoudial model problem.

Q: x²+8x+15 Consider the function f(x): = x+1 a. Find the first derivative. f'(x)= b. List any critical…

A: Note:-Since you asked multiple sub-parts questions, according to our policy we can solve only first…

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) = x² + y² subject to the…

A: We know, that

Q: Use Lagrange multipliers to find any extrema of the function subject to the constraint x² + y² ≤ 1.…

A: The given function f(x,y) = e-xy/4   Extrema of the function subject to constraint x2 + y2 = 1…

Q: Notice this is the graph of the derivative of g not the graph of g itself. Answer the following…

A:

Q: Use the compound interest formula, A (t) = P(1 + 77) n After a certain number of years, the value of…

A: The value of investment is : $ 15903.61Explanation:

Q: Compute the mean, median, and mode of the data sample. (If every number of the set is a solution,…

A: The objective of this question is to calculate the mean, median, and mode of the given data set.…

Q: Use the One to One Property of Exponentiation to solve the following exponential equation. Input…

A: 23x= 41+xWe have to find value of x using one to one property of exponential

Q: 2. (Series) Determine if the following series converge or diverge. If it converges, find the sum. i.…

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

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Given that when air expands adiabatically (without gaining or losing heat), its pressure P and…

Q: Use a half-an le formula to find the exact value of tan 105°. tan 105° = 0 G

A: .

Q: Find f'(x). f(x)=5x-4ex

A: f′(x)=5exe−1−4exExplanation:

Q: Deriving Snell's Law from an Optimization Problem Refraction is a physical phenomenon that happens…

A: Please find the below attached solution as per the suggested steps.Explanation:

Q: Find X1 and X2- -2 - 4 X1 -2 3 x2 H + 19 -9 3 17 X1 X₂ = 38

A:

Q: Below is the graph of the function f (a) and a table of the graph of g (a). Solve the equation f…

A:

Q: Find the derivative off with respect to x of f(x) = In x 10 The derivative of f with respect to x of…

A: The logarithmic formula: ln⁡xm=mln⁡x .The derivative of logarithmic function: ddxln⁡x=1x

Q: #10 For the surface x³-2xz+y4+1=xy do: (a) Find the tangent plane at point (1,1,1),, Find…

A: (a) Equation of tangent plane at point (1,1,1) is: y=1(b) Equation of normal line at the point…

Q: Write the corresponding rectangular equation for the curve represented by the parametric equations…

A:

Q: 2 #12 Given f(x, y, z) = 3√ √ x²+ y²+z² (a) Find the linear approximation L(x, y, z) near the point…

A: a.) The linear approximation is L(x, y, z) = 2√2 + (-1/√2)(x + 2) + (1/√2)(z - 2)b.) The linear…

Q: (a) Evaluate the surface integral ff z² dS, where S is the upper half of the sphere x² + y² + z² =…

A: For part (a), the surface integral evaluates to(−332π​). For part (b), the surface integral…

Q: Compute the mean, median, and mode of the data sample. (If every number of the set is a solution,…

A: The objective of this question is to calculate the mean, median, and mode of the given data set.…

Q: Use undetermined coefficients to find the particular solution to y"-3y-10y=4e³t Yp(t) =

A:

Q: Find y" if y= -4 cos x OA. y" 4 cos x

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: (a)f(6)=4(b)limx→2​f(x)= Do Not Exist.(c)limx→6​f(x)=2(d)limx→2−​f(x)=1Explanation:Step 1:Step 2:…

Q: If x3+y=7, find the value of d²y dx2 at the point (-1,2). d2y The value of at the point (-1,2) is…

A: Given:To find:The value of  at p[oint (-1, 2)

Q: Find dy dx y=9lnx+5 loggx

A: dy/dx=9/x + 5/(x*ln9)Explanation:Step 1: Step 2: Step 3: Step 4:

Q: - #13 Given z= f(xy) = ex+2y= en (-x-y) +xy² a) Evaluate f(-2, 1), (b) Estimate the "error" in the…

A: a) -1b) (-1.15,-0.85)Explanation:a)  b)

Q: Use the Chain Rule to find Əz/ǝs and Əz/ǝt. z = x5y5, x = s cost, y = s sin t Z Əz || дл at ||

A: Answer is given below.Explanation:Step 1:--Step 2: Step 3: Step 4:

Q: You are looking at a balloon that flies straight up. Your horizontal distance from the balloon is…

A: Let the height of balloon is  m and x m be the horizontal distance The figure

Q: Let f(x)=3x³-5x²-2, x≥ 1.5. Find the value of df at the point x=248 = f(5). dx df The value of dx 1…

A:

Q: Find an equation of the ellipse with vertices (0, 3), (12, 3) and eccentricity e = Select one: a.…

A: Vertices:eccentricity, e=