4 For which values of a e R is the function f(x + iy) = (a²x – axy)+ i ax? + ay an entire function?

Q: 2x If f is the function given by f(x) = Vi? -t dt , then f'(2) =

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Q: If F(x) is an antiderivative of x2 + x', then what is the value of F(1) - F(-1)? A) -1 в) з c) o

A: We will find the value.

Q: 4. Let f (x) = e-w2 dw csc-1 x Then f'(V2) = A) 2 –e 16 B) 1

A: Here we have f(x)=∫csc-1x∫2x2sinπ16t2dte-w2dw ....................... (1) We have to find, f'(2)=?

Q: 3) Let f(x) represent the path of a particle. x* 1 f(x) =+ x 2 1 16 2x2 Suppose the particle starts…

A: The arc length = the distance covered along the curved path f(x).  A = the arc length  A =…

Q: 2. Find and classify all the extrema of the function f(s, t) = (4s² + 2t²)e¯

A: 2

Q: Find the values of a and b that make the following function dif- ferentiable for all x-values. Jах +…

A: To be differentiable at x=-1  The function must be continuous at x=-1 So we plug x=-1 in both…

Q: 3 Consider the function f(x)= 2x +1 a. Write the linear approximation to f(x) at x = 4. b. Use your…

A: Explanation of the answer is as follows

Q: If F(x) is an antiderivative of y-2+ x-1, then what is the value of F (1) -F(-1)? O 3 -1 O-2

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Q: f(x) dx = 4, Suppose f(x) dx = 3, g(x) dx = 2. Which, if any, of the following statements are true?…

A: Given:

Q: Consider the function 8 · + 9. xy f(x, y) In which direction does the function f(x, y) increase most…

A:

Q: 17. Find the linear function f(x) that is parallel to 4x + 3y = 6, such that f(0) = 7.

A: Given function, 4x+3y=6, That is 3y=-4x+6 y=-43x+2 compare to y=mx+c Therefore m=-43

Q: 5. Find the most general antiderivative of the following function. 2x² +5 f(x) = x² +1

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Q: 1.4 For which values of a €R is the function ax? f(r + iy) = (a²r - ary) +i + ay ) 2 tire funetion

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Q: 4. Find three functions f, g,h that satisfy: f(g(h(x)))= +2 Vx?

A: Given,             fghx=1x2+2

Q: ax? If f(x) = if x > 1 then the bæ + 2 if a<1 values of a and b such that f is differentiable on…

A: For function to be continuous

Q: If F(x) is an antiderivative of x2 + x1, then what is the value of F(1) - F(-1)? O -2 O -1

A:

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: the impermissible value of x for the function y = 1 / (e ^ 2x-1) is: a) 1 b) 0 c) 1 d) e

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Q: Q3) A) If you have three functions: f (x) = x² – x %3D | g(x) = 3x – 1 %3| w(x) = x² – 2 So, find…

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Q: Please show step-by-step solution!

A: According to chain rule the derivative of the f(g(x)) is [f(g(x))]’=f’(g(x)) * g’(x)

Q: At what value of x does the function f(x) =3 x-Vx change from decreasing to increasing? 1/9 1/8 1/3…

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Q: Find numbers a and b such that the given functiong is differentiable at 1. |ax³ - 3x if x 1 a = b =

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Q: Q2: Let f(x) = 2x e-,x> 0 and Let Y = X2.Find G(y)and g(y). %3D

A: Implicit functions are the functions are not directly expressed, these are always expressed in terms…

Q: Let f(x,y) = In ( x2 + y). If fy(2,a)=fy- 1, 2), what is the value of a? а. 3 O b.7 О с. 8 d. 6 O e.…

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Q: I. Differentiate the given functions: 1. f(x) = 3e* – 9* 2. f (x) = In V6x +7 3. f(x) = x²e* %3D

A: Solution:Given : 1. fx=3ex-9xlet f1(x)=3ex and f2(x)=9xtherefore f'(x)= f1'(x)-f2'(x)f1'(x) = 3ex…

Q: Q3) prove that: fa+¹h f(x).dx h 2h 4h - = 3 [ƒ (a) + f(a + 4h)] + f(a+2h) + [f(a+h) + f(a + 3h)] 3 3

A: Introduction: Numerical integration is a word utilized in evaluation to explain a set of strategies…

Q: df If f(x) = e" In x, then, when x 1, is dz nonexistent O 1/e O 2/e e

A: Answer is below

Q: Q1- If we have the following function: f(x, y) = 5 x8 y/3 + In x + e*y find fxx fyy f xy, and f yx…

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Q: Find h'(2), given h(x) = f(g(x)), f(u) = u² – 1, g(2) = 3, and g'(2) = –1. ||

A: According to the problem, we get

Q: 1. For what value of x does the function g(x) --x + 2x strictly concave downward? %3D 3. B. x > 1 A.…

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Q: If F(x) is an antiderivative of x2 +x', then what is the value of F(1) - F(-1)? A) -1 B) -2 D) 3

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Q: 3. Consider the following function: z = f(x, y) = e²+24 (3x – y)

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Q: or function By – k1 z) + ay (kz y + z) onal, then the values

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Q: Consider M(x, y)+ N(x, y) · = 0. M and Fy (a) Suppose we can find a function F example of such an…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: This function f(z)=(x^3-3xy^2)+i(3x^2 y-y^3) is differentiable O True False

A: Given :f(z)=x3-3xy2+i3x2y-y3

Q: If F(x) is an antiderivative of x2 + x1, then what is the value of F(1) - F(-1)? 3 -2 O -1

A: Solved below

Q: If F(X) is an antiderivative of x2 +x', then what is the value of F(1) - F-1)? (А) -2 В) -1 D) з

A: Given: F(x)=∫x-2+x-1dx So, by the Fundamenetal theorem of calculuas: F(1)-F(-1)=∫-11x-2+x-1dx Now,…

Q: 5 Given that y is a function of x, differentiate the expression (x + y) with respect to x. Enter D…

A: The objective of the question is determine the derivative of the given function.

Q: 2. Consider the three functions below: S(z) = 2z S(z) =r S(x) = 2"

A: fx=2x,fx=x2 and fx=2x (a) Take the value of x as -2,-1,0,1,2,3. x fx=2x fx=x2 fx=2x -2 -4 4 14…

Q: The function y=C, e° is the general solution of a) O y"– 2 y' – 3 y = 0 b) O y" +2 y' – 3 y= 0 O y"…

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Q: 2 ,xs2 f(x) dx, where f(x) is denoted by f(x)={ 3x , x>2

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Q: 4 For what value(s) of x is the function f(x) 2x2- 6x | NOT continuous? A. x=0 andx= 3 B. x = 3 only…

A: We need to find points at which f(x)=42x2-6x is not continous.

Q: 2x he function f (x,y) = is said to be homogenous to what degree? A) zero B) one c) non-homogenous…

A: Topic:- calculus

Q: Q4: Find the most general antiderivative F(x) of the function f (x) —D 2х7 — Зх5 — х?. - A F(x) = x³…

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Q: This function f(x + iy) = (x2 +x - y²) + i(2xy + y) is differentiable ? False O True

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Q: 11.What value of x is the function f(x) = Vx2 - 3 continuous? Α. x =0 B. x = 1 C. x = -3 D. х 3D -2

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Q: If we use trapezoidal rule for a function f(x) = 1 then the approximate of x +2 f(x)dx is Select…

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Q: 7. Which function(s) have/has a zero at x = -5? a. y = 2*+5-1 b. y = x² -5 C. y = |x - 5| d. y %3 (x…

A: We have to find the function

Q: Find a function g = g(t) such that %3D s +3 L(g) = s2 – 2s + 5 -

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Q: y2 For function f (x, y) = x2+1

A: