Refer to the figure to determine f'(a) for a = 1, 2, 6, 8. y 5- 4 3+ 2- 1- 1 2 3 4 5 6 7 8 9 (Give exact answers. Use symbolic notation and fractions where needed.)

Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

A:

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

A: Given query is to find the derivative of the expression.

Q: Compute P(0), and find the exact values of the six circular functions given that 0 = – 135°.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: Find the devivative of f cx) = by Hhe de filzifion.

A: Here we differentiate the given function by it's definition.

Q: Estimate the value of f, (1 – r 4.r + 2x) dr using single application Simpson's 1/3 Rule.

A: This is a Numerical Analysis problem.

Q: Find fry for f(x, y) = In(x – y).

A:

Q: Take a look at the derivative of the integral * S (6t2 – 5t + 2) dt. (6t² dr Evaluate the…

A:

Q: 3. Compute the first four derivatives of f(x) = sin r + cos r. Try to find a pattern and guess the…

A: we have to find the first four derivative of f(x)=sinx + cosx and then we have to find the n-th…

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

A:

Q: For f(x) = sinx, compute f ' at x = 0, π/6 , π/2 , 5π/6

A: Given, fx=sin x

Q: Suppose f(x) = – 2x – cos r. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

A:

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

A:

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: 1 F (s) = s (s +1) %3D

A: Given: L-11ss+1

Q: Calculate the derivative by expanding or simplifying the function. s(t)=(1 – 2(5t))/(5t)^1/2  (Use…

A: We have to find

Q: 5. Given that f (x, y) = sin y, determine fy(x, y).

A:

Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

A:

Q: Suppose that f (1) = 2 ,f (4) =7, f '(1) = 5, f '(4) = 3and f" is continuous. Find the value of ∫1…

A: Given f1=2f4=7f'1=5f'4=3 f''x is continuous To find value of ∫14xf''xdx

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: Suppose that f(1) = 2, f(4) = 8, f'(1) = 10, f'(4) = -3, and f" is continuous. Find the 4 value of…

A: We have to find the value of the given integral.

Q: The graph of the function is concave downward on the interval(s): O (-00, co) O (-0, d) O (-0, d] O…

A: Find the first and second derivative of g(x) and find the interval for which g(x) is concave…

Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: ) Differentiate f(r) = In(v²) + In(10). Hint: Think before differentiate :) you

A:

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

A:

Q: 2. For which values of a is f(x) differentiable on R?

A:

Q: التاريخ الموضوع Find The approximate value of f(x) at X=1-2 whereof is defined over The period 1.7]…

A: The given table is To find: f(1.2)

Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

Q: Suppose f(x, y) = (2æ)" + 3y". Find f# (1, 1), fy(1, 1), and fyy (x, y)

A:

Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

A:

Q: Evaluate F. dr where F(x, y, z) = (3.75yz cos(xyz), 3.75xz cos(ryz), 3.75xy cos(xyz)) and C is 1 1…

A:

Q: Suppose that  f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 5, and f ''  is continuous. Find the value of…

A:

Q: If the relation x z² - 5xy z-x2-y 0 defines z as a differentiable function of x and y. By using the…

A: Solution

Q: Suppose that f: R2R is a function given by S x²+y² f(x, y) 0 for xy = 0. Show that f(x, y) is…

A: We have to show the given function  f(x, y) is continuous  at ( 0,0)

Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

A:

Q: If z = f(x,y) = 3x^2 - xy , get the total differentiation of z if (x,y) change from (2,3) to (2.5 ,…

A:

Q: The function f (x) ,x € [-27, 2n] is continuous on: 1-cos x

A:

Q: Let –1, -T<¤ < 0, 0, 0 < x < T. f(x) = * = 0 1,

A:

Q: Let f(x, y) = x 3y - 4 . Use Eq. (4) to estimate the change fl.f = f (2.03, 0.9) - f(2, 1)

A: Consider the given equation as fx,y=x3y-4 Simplify as fx,y=x3y4

Q: Suppose that f (1) = 2, ƒ (4) = 7, f' (1) = 5, f' (4) = 3, and f" is continuous. Find the value of…

A: Given data: f(1)=2 f(2)=4 f'(1)=5 f'(4)=3 The objective is to find the value of ∫14xf''(x)dx Apply…

Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: