F:R³ → R² defined by ED- 3x1 + x2 - 6x3] -X1 + x2 + 13x3] F

Q: Let flx)-4x H2 %3D

A: Topic = Function

Q: Show that r: y = 3. 2n

A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: 8. Given f(x) = -4x5-3x3 + 4x² -7, use synthetic substitution to find f(-3). %3D

A:

Q: What is (go f)(x) if f(x) = 3x – 1and g(x) = 4x? + 9? %3D %3D (go f)(x) = 24a2 – 25 O (go f)(x) =…

A: note: (g o f) means g(f(x)).

Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: The critical numbers of f(x)=-x' +3x+2 are:

A: 3rd option correct

Q: Use the IVT to prove that r-5x2 + 2x = -1 has a solution. %3D

A:

Q: Find the critical points of f(x) = x³ - 3x² - 24x. %3D

A:

Q: Show that 22x-1 Г(2x) - r(x) r

A:

Q: The domain off(x) = 3-x is 1-x2 %3D 1. R 2. R/{1,-1} 3. R/{3} 4. (0, ∞)

A: Domain: The domain of a function is the set of all input values for which the function is defined.…

Q: Let f(z) = (3z + 8) %3D 6. f'(z) = (3x 8)4 6. f'(3) = (3x 8)4

A: See the details solution in below

Q: 2y = xx -1-In(x+vx² -1)+c

A: Given the family of curves is 2y=xx2-1-lnx+x2-1+c. Find the orthogonal path of the above curve.

Q: Let a > 9 be a constant. Evaluate 3z2 + 30x + 30 + 4a dz (3x + a)(x² + 6x + 10)

A:

Q: 2dx Evaluate (x – 3) Vx² – 6x + 5 -

A:

Q: D. Differentiate the following. f(x) = 4x5 - 5x +x +8 g(x) = * --*+x' + v2 c. h(x) = V9x° + V7x7 +…

A:

Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: Show that Live - de = In(V5- 2). -1 Vx2 + 2x +2

A: We need to show that, ∫-11-dxx2+2x+2=ln5-2

Q: Use the subst ition =x+y=0 4x-3y=0 By Your answer is

A: -x+y=0  ----->14x-3y=0  ----->2from equation1-x+y=0⇒y=xsubstitute y=x in equation 24y-3y=0y=0

Q: on f(x) = 8x¬' at x = 3. %3D

A:

Q: on f(x) = +9x is %3D 2)

A: There are multiple questions, as per company policy kindly ask other questions separately.    Given

Q: show that flzi2)= f (2)f(2).

A:

Q: The antiderivative of the function f(x) : .2 + 11x³ is, 4 - + 2.8x4 + c - -11 + 1.2x* + c -5 + 2.8x…

A: As we know that if we need to find the antiderivative of f(x);   So,   ∫fxdx=Fx+C   From the given…

Q: Evaluate f"(c) at the point. 9) f(x) = In (4x - 3), c = 1 10) f(x)=3x2-3, c=1 3x - 4 11) f(x)= 4x-3'…

A:

Q: Investigate the based on linearization 3 x = x₁ - x₁²³²+x₂z xr 394 - 292 6 Ac

A: This is a question of equilibrium and stability.

Q: Show that (x) = In/x² -1- In /3, f"(x) = 1 and (2) = 0. .2 x* - 1 | Justify your answer.

A:

Q: 3. Differentiate. x²e* f(x)%3= x² + ex

A:

Q: 30x +31x2 - 25x 6 Ehe domain of f(x) = \ 1213 59r2 11la + 30

A: Given function is fx=30x3+31x2-25x-612x3-59x2-11x+30.

Q: Calculate the real values of x and y such that (x+y)3 is bigger than 8?

A: Given, x+y3>8

Q: 6 4 Verify that for f(x, y) = 3x°y* - 4x°y°. дх ду ду дх of

A: Given problem:-

Q: Let f(z) = 4z +1 f(2) =

A: Given  f(x)= 4x+1

Q: 2. Use a trig substitution to evaluate S dx x³√²-16' x> 4.

A:

Q: 2 Let f(x) = V5x² + 4x + 8 f'(x) = f'(3) =

A: Given : fx = 5x2+4x+8

Q: Suppose 7x + 2 f(x): %3D x2 + x - 2 Then A + x + 2 В f(x): %3D x - 1 where A = and B =

A:

Q: 4. For f(x) = 3x² + 5 and g(x)=7x-2, %3D %3D

A: answer is in next step

Q: 21. If f(x) = 2x - 1 and g(x) 3x + 5, what is f(g(5))? %3D %3D

A: Given, f(x)=2x-1 g(x)=3x+5 f(g(5))=?

Q: What is f'(3) if f(z) = z/2z - 2 I.

A: d(xn)dx=n(x)n-1

Q: 7. Use f(x) = -2x + 1 and g(x) = x² + 3x + 2 to find (f8) (2). %3D %3D

A: We can solve it as below

Q: 5lim V3+x-J3 8→0

A:

Q: 11. If f(x) = 2x² + 7x + 3, show that ƒ(b + 2) = 2b² + 15b + 25. %3D

A:

Q: f (2) 2. Find if Ar) -(1-x²)(* -1) =

A:

Q: • The domain of f(x) 3-х is 1-x2 1. R 2. R/{1,-1} 3. R/{3} 4. (0, co)

A: Domain: The domain of the function is defined as the set of all input values for which the function…

Q: 23) The domain of f(x) = Vx + 3 is

A: Consider the function

Q: Verify that * / II 21 ?х ду 224 ду ох - for f(x, y) = 4x4y3 - 6xy5.

A:

Q: O Express : 2 as a linear combination of

A: By using definition of linear combination

Q: Sketch the nullcline for: x' = 4 - y2 + x2 Explain.

A:

Q: Compute x-x where x=i-2.

A: For the given value of x x =i-2  x3-x is evaluated as shown below

Q: Find 2 for all of: 1- y = xvInx 2- y = 3 x(x-2) x²+1

A: