1. Evaluate •3 f(x)dx if |x², f(x) = x < 2 За — 2, х 22 x > 2 -

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: a = &lt; x, y, 1 &gt;b = &lt; 1, -1, 3 &gt;|a| = (14)^(1/2)/2a•b = 5Find all possible values of x…

A: As we know dot product and given information

Q: Given the function below f(x) = 3 x³ – ²x² − 18 x + 3 a) Differentiate the functionƒ(x) = 3 x³ − 2…

A:

Q: 1. S (x+ ) V dx 1. x5/2 + 2x1/2 + C 2. 6x 2/3 + C S dx 2.

A:

Q: 3. (a) Which of the following functions have 5 in their domain? f(x) = x² - 3x *- 5 h(x) = Vx - 10…

A:

Q: 3. When is the function increasing and when is it decreasing? f(z) = re==z3)? xe 2 f(x)=xe 4X2)

A: Solution:

Q: If f(x) 2 0, then [ flx)dx Select one: O True O False

A: F(x) is postitive so area under the curve is above x-aXis so it is positive.

Q: 6) L (x- 3)(x + 2)? dx

A:

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: 6. (a)f dx x(x +3)2

A: To evaluate the given integral

Q: r 4-5x 3. f(x)=- ; f'(-1)

A:

Q: 1. f(x² − 3x + 7) + (2x − 3) dx

A: In this question, we need to integrate the given function.

Q: 5. f() = {x? - 4 U x* -3 Evaluate f(4), f(0), f(-3) and f(-2/3) }" -2 if x = -3'

A: The objective is to evaluate f(4), f(0), f(-3) and f(-2/3).

Q: CLX 5) Let f(x)=√√x³- 4x + 1, f(3) = 4, find (f¹)'(4).

A:

Q: 4 If f(x) = ln(2x² – 3) then f'(x) =? - 2x a) 2x2 – 3 - 4x b) 2x2 – 3 2x c) 2x2 + 3 -4x 2x2 – 3 -…

A: f(x) = ln(2x² - 3) So, f'(x) = 1/(2x²-3) × (2x²-3)' So, f'(x) = 4x/(2x² - 3) .... Option (b)

Q: 3 - dx x² – x - 2 (1) (ii) fx'e* dx

A:

Q: x³ + x 10) √ (x²+ + 2x² + 5) dx

A:

Q: S dx b² +x4 - Evaluate

A:

Q: 21. What is the domain and range of f(x) = V– In x ?

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: If f(x)=(2/x+3) g(x)=(1/x) To Find (f o g)(x)

A: Given fx=2x+3    gx=1x

Q: [2, 03 b) If f(t)={ , find L{S(1)}.

A:

Q: 5. Determine f,(x); f(x) = x*², x > 0

A: We need to find out first partial derivative

Q: 04. + 2- 3r-11 (a) Show that -0 can be rearanged as

A: Given that: f(x)=x3+2x2-3x-11

Q: Sketch the following functions. Show all your work. N a) Domain b) Intercepts c) Symmetry d)…

A:

Q: R ,,D المناسبة ل لداله الاتية : س / أختار قيمة x-2 f(x) = x+2

A: Root of the function is 2.

Q: . Evaluate S (-+ 3e* ) dx

A: We have to Evaluate  ∫ {(1/√x) - (2/x) + 3ex} dx = ∫(1/√x) dx - 2 ∫(1/x) dx + 3 ∫ex dx

Q: Evaluate 7x 11 √(x - - − 1)(x – 3) - - - dx

A:

Q: 2. (10 points) Evaluate 3x² (x3+5)² dx (using substitution)

A: Step 1:Step 2: