For a > 0. let f (x) be an integrable function given with f(-3)=0.f(-2) =a and f (6) = 4. Find the value of a, if we know that C [₁ƒ (2x) ƒ' (2x) dx = 3. O A)1 2 O 83 0 C3 2 O 012 O E5 2

Q: Given the function f(x) =4x3 – 39x²+ 90x+ 2; which of the following describes its absolute extrema a…

A: We will find critical points to check for absolute maxima

Q: Find three rational numbers between the following pairs of numbers. 8 and 0.89 a. 8 b. and 0.89…

A: Given that: (a)89 and 0.89(b)89 and 0.89

Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

A:

Q: 2) Find a value of c for which f (x) is a pdf on the f(x) = cx + x², [0. 1]

A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

Q: 1) Consider the function f(x): = 5x² - 4x +7 Find a number c in the domain such that f (c) = defined…

A: Given: fx=5x2-4x+7 for x∈1, 4 To be find c∈1, 4 such that fc=13∫14fxdx Integral of ∫xndx is given by…

Q: If f(3) = 11, f' is continuous, and • f*F(x) f(4) = f'(x) dx = 15, what is the value of f(4)?

A:

Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

Q: Let f(2)= iz³ + cos(z²) z² +1 i. Find f'(z). ii. Evaluate ƒ'(–2i) and simplify. iii. State the…

A:

Q: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

A:

Q: Suppose f is a function for which f'and f" exist. You are given that: S(0) = 1 S'(0) = 5 %3D %3D…

A: here we use the integration by parts see below the answer and calculation

Q: Let f(x) and g(x) be differentiable functions. Fill in the blanks with the appropriate function or…

A: To fill in the blanks with appropriate function or expression.Note: Since you have posted multiple…

Q: Find the derivative. 1 y = _x3 + 3x + Væ 2 Ody dx O Ody dx || ip O 32 y=2x2 +3 + 2x 32 || 2 X +3+1/x…

A:

Q: Evaluate f(1) dz, where S7a, 0<<1 f(z) = 4x2, 1<< 2. f(z) dr =

A:

Q: Let f(x) and g(x) be differentiable functions satisfying f'(x)g(x) = – f(x)g'(x), Vr. If f(1) = g(1)…

A: Given f(x) and g(x) be differentiable function. f'(x)g(x)=-f(x)g'(x)    ∀xf(1)=g(1)=5f(5)=1 To find…

Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: dz 6. If z²x²y (where x, y, and z are positive), then what is dt dy dt e C given that dz dt BU Font…

A:

Q: Let f(z) be a differentiable function on the interval [-6, 2] such that f(-6) = --4 and f'(z) < 2.…

A:

Q: 12x + 3 11x +9

A: We will solve the following.

Q: Let f and g be functions differentiable on R. with Find f(x)|x=2= d g(2) = 2, 9(x)\x=2 = 4, de…

A:

Q: The derivative of y = 4cosxsinx is: ○ a) yl= 4(1 — 2 sin² x) b) y/= -4 sin x cos x c) dy = 4 sin x…

A: To determine the derivative of the following function.

Q: II (20’) Let X={1, 2, ., 16} and define function f(x)=rx for all x E X where rx is t remainder when…

A: Let X=1,2,.....16 defined by fx=rx  ∀x∈X We know that, "If a and b are two integers where a≠0 then…

Q: Let f be a differentiable function such that f (3) = 2.345 and f' (x) = ln(x² + 1). What is the…

A: solution:-f'(x)=ln(x2+1)f(x)=∫ln(x2+1) dxusing integration by partsf(x)=∫1·ln(x2+1) dx=ln(x2+1)∫1…