b) For what values of p and q will pr + q, f(1) = 3 pr + r+ 2q, ¤> -1, - { I<-1 be differentiable for all values of r?

Q: (c) Prove the inequality I +y +x > Vryz 3 if x > 0, y >0 and z > 0.

A:

Q: Q4/ if f(x.y)=x-y and g(x.y)=3y prove V2) gVf-fVg g? %3D

A:

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

A:

Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

A:

Q: Determine the intervals in which solutions are sure to exist. t(t − 2)y(4) + e¹y" + 6t²y = 0 Enter…

A: As per the question we are given a forth order linear differential equation as : t(t-2)y(4) + ety''…

Q: 4. Find f'(x), if f(x) = (2x – 8x²)-²(3x + 1). 5. If y is a twice differentiable function and x cos…

A: Differential equation. Solving only first ques as per bartleby guidelines.

Q: Q.4 Given that f(2) is analytic at z = 0 and that f () =, n = 1, 2, 3...,find f(2).

A:

Q: hich z ∈ C the function e^(1/z) is holomorphic?

A:

Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

A:

Q: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: 4: Find the approximate value of f(-2.001, 1.002) where f(x, y) 3x?y + y? – xy +1

A:

Q: Determine the linear approximation of f(x) = x² at x = 1. a. y= 2x +1 O b. y = 2x - 1 O c. y=- 2 x-1…

A: Given: f(x)=x2, x=1 To find: Linear approximation at given point.

Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: Use Euler’s method with n = 2 on the interval 2 ≤ t ≤ 3 to approximate the solution f(t) to y′ = t -…

A: Given, y'=t-2y y(2)=3

Q: Suppose that f(z, y) = z² - zy + y? – 5z + 5y with z? + y? < 25. 25 1. Absolute minimum of f(x, y)…

A: We have to solve the maxima minima problem.

Q: x?y" – 4xy' + 6y = 0, y(-2) = 8, y'(-2) = 0

A:

Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

A:

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

A:

Q: Given the equation y In (x? + y² + 4) = 4, evaluate dy Assume that the equation implicitly defines y…

A:

Q: For function f(x,y) to have maximum value at (a,B) IS 1) rt – s>0 and r0 and r>0 3) rt – s?0 and r>0

A: for function f(x,y) to have maximum value at (a,b) is rt-s2&gt;0,r&lt;0

Q: f({x, y))) for all c e R and all (x, y) E R?

A:

Q: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

Q: Find a2z given that z is a differentiable function of x and y, and xz + yz3 = 2 + x²e♥

A:

Q: 41. For ), find all values ofx and y such thatx,y)=0 simultaneously. and yr.y)=0 f(x, y)…

A:

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

A:

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

A:

Q: 1. Given f(x, y) = 4x³y², evaluate f;(1, y) and fy(x, 2).

A: We know that partial derivative of f with respect to x is denoted by fx  and partial derivative of f…

Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: 1 Find the length of the curve f(x) + from x = 2 to x = 4. %3D 6. 2x

A:

Q: With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are…

A: Given two curves are y=c1x2+k   and x2+2y2-y=c2  , where c1 &amp; c2 are arbitrary constants. Let us…

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

A:

Q: Let f(x,y)=2x²+y²-8x-6y+12. 1- Find Vf at (1,1). 2-Find the extreme values of f.

A: Given data: The expression for the given function is f(x,y)=2x2+y2-8x-6y+12. 1) The given point  is…

Q: %3D 23. f(x, y, z) = 2x + z? subject to x² + y? + 2z? = 25

A: Lagrange's Multipliers: The Lagrange method is used to maximize or minimize a general function…

Q: Determine the linear approximation of f(x) = x* at x = 1. а. у %3D 4x - 3 O b. y=- 4 x - 3 О с. у-…

A:

Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

A:

Q: x² + 5x ,14.f(c) = = 14 f(x) on interval %3D %3D x - 1

A:

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

A:

Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: 2. Use the secant method to estimate the root of f(x) = a° + a³ + 3. %3D By starting with the…

A:

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

A:

Q: 2: find fr, fy, and fz. 9 f(x, y, z) = 1 + xy? - 222 5 f(x, y, z) = x - Vy² + z?

A: (a) Given f(x, y, z) = 1 + xy2 - 2z2 So fx = ddx(1 + xy2 - 2z2)    = ddx(1) + ddx(xy2) - ddx(2z2)…

Q: 1. Determine if if r2 /2r is differentiable at r 2.

A: First check for continuity then the derivative if both exist then function is differentiable.

Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.