Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

Q: Sketch the domain of the f(x, y) = ln((x² + x² – 4)(16 – x² – y²)) |

A: Recall:  Domain of the function:           The domain of the function is the set of all values for…

Q: Find the antiderivative F of f(x)=4-3(1+x^2)^-1 that satisfies F(1)=-2.

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Q: Find the constant a such that the function is continuous on the entire real line. [ 5x², x 2 1 x < 1…

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Q: Let f(x)=x2+2x. Find all values of c in the interval [−2,0] such that f′(c)=0.

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Q: Find c such that the function f(エ) 8x- 20 I > C is continuous everywhere.

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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Q: Find the constant a such that the function is continuous on the entire real line. (x) = {4x?, ах —…

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Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

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Q: (c) Show that f(x)>0 for all values of x, x # -2.

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Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

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Q: Find the constant a such that the function is continuous on the entire real line. (5x2, ах — 3, x 2…

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Q: Let h(x) where f(x) = In(3x² + 2x + 2) and g(x) = -2x. What is h'(x)?

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Q: Find the linearization L(x) of the function at a. f(x) = x4 + 6x2, a = −1

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Q: Prove from the definition of differentiability that the function f : R\{3/2} → R f(x) = 3 – 2x is…

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=3x−2,g(x)=2x−3, and h(x)=−2x2+4x, what is k′(1)?

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Q: Use the Intermediate Value Theorem to show that f(x) = x2 + x − 2 has at least two zeros in the…

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Q: The function f(x) = x²e*- ex has a root in [0,2]

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Q: Determine all critical points for the function. f(x) = x2 + 6x + 9 %3D

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Q: The function f(x) =x -x² – 2x – 1 is increasing over: %3D

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Q: let h(x) = f(x)/g(x), where f(x) = -3x^2 + 2x + 2 and g(x) = -2, what is h'(x)?

A: Given  hx=fxgxwherefx=-3x2+2x+2gx=-2 To find the derivative of h(x) Quotient rule is to be used…

Q: Find a function f(x) such that f'(x) = 6x² – 3 and f(0) = 1 - %3D f(x) =|

A: Given:     f'(x) = 6x2 - 3    f(0) = 1

Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

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Q: Show that the function f(x)=x3−3x2+6x−1 is strictly increasing on R.

A: Let us find f'(x) using the power rule

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: (a) g(x) = x + 1 x-1 (using the definition)

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: Prove that if f(x)=c (a constant function), then f'(x)= 0

A: Given query is to prove that derivative of constant function is zero.

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

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Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: Find ao of the function f(x)=(-x)², 0≤x≤ 2π

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Q: 1. Let f(x) = 4 – 4x?. Verify that f(r) satisfies the conditions of Rolle's Theorem on the interval…

A: 1. The Given function is f(x)=4x-4x2 Diff. with respect to 'x' f'(x)=ln(2).22x+1-8x

Q: Use the Intermediate Value Theorem to show 11. f(x)=2x' +3x-1 has a zero between a = 0 and b = 1.

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Q: The domain of f(x) = /1 – I In(x) is %3D

A: The domain is the set of all possible x-values which will make the function give real y-values as…

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1&lt;x≤1x2+bx,x&gt;1

Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

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

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Q: Find a number c that satisfies the conclusion for f(x) = x + x-1 on the interval [0, 2]

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Q: Let f(x) = Vx - 1 g(x) = v2- x obtaind )(x), and the domain of (x),

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Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x&lt;1

Q: The domain of the finction f(x, y) = In(-x² - +1) is:

A: The domain of a function is the range of the values that can be input into the function. The…

Q: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

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Q: Let h(x)=f(x)g(x) where f(x)=2x^2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)?

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Q: Consider the function f defined by the formula ( ax2 + bx – 3b if x 1. Determine the values of a…

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