Answer this question by showing all work and formulas used to solve: 7. Pick the correct answer and explain your answer with words: [2C] Your sibling states “If you finish homework, you can borrow their car". You know this means, "If you don't finish homework, you cannot borrow their car". Your mathematician friend says, “If f is differentiable at x, f is continuous at x". This means: a. if f is not differentiable at x, f is not continuous at x b. if f is not continuous at x, f is not differentiable at x c. knowing f is not continuous at x , does not give us enough information to deduce anything about whether the derivative of f exists at x.

Q: f(x, y) = 2 sin x+ 3 cos y; R is the square region with vertices (0,-7/2), (7, – 7/2), (7, T/2), (0,…

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Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

A: We have to find the value of x such thatWe know that

Q: Is the following statement correct? If the function is continuous on R then the constants a and b…

A: It is not necessarily correct that every continuous function on R take the value 2& -2…

Q: Complete the sentences below to obtain true statements. Use the following words: increasing",…

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Q: Consider the following argument: If f(x) is a differentiable function, then it must be continuous.…

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Q: f(x, y) = x - y“; R is the disk x +y < 1.

A:

Q: 4. Evaluate Si (+) dydz

A: the given integral is ∫14∫12xy+yxdydx therefore,…

Q: Which of the followings are the inflection points of f(r) = Inz I. x=0 II. x=e III. x=1 IV. ¤ = e 2…

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Q: 2² –4 if æ 3

A: The given function isf(x)=x2-4x-1if x&lt;2ax2-bx+1if 2≤x&lt;34x-a+bif x≥3

Q: 26. ƒ(x, y) = ye*; R is the rectangular region with vertices (0, 0), (In 2, 0), (In 2, 3), (0, 3).

A:

Q: 5. Which function has both domain and range of all real numbers? a. y = x2-5 b. y = (x + 2)3 c. y =…

A: To find  the function having domain =R and range =R.

Q: Given f(x) = 3– 2x – x, Determine each of the following. C. a.) f(-6) b.) fG c.) f(r*) d.) f(x-1)…

A: Topic = Functions

Q: . Determine if y is a function of x in x = y? + 5.

A: Given equation - x = y2+5Let's solve for y =- y2 = x-5y = x-5       ........(1)

Q: A) Find for the following functions: 5x+1 1- y = 2 va 2- y = v2t + 2t t = x2 - 3

A:

Q: What values must a and b take for f to be continuous everywhere?

A: Given that the function fx=ax1+4x2 ,      x&lt;0b    ,                     x=0tan-1xx ,…

Q: d) Consider f(t) = bt, where t&R and b ER such that 0 by [Select] e) 5 log25 k² = k where k denotes…

A: To label the following statements as T for true or F for false.d Consider ft=bt, where t∈R and b∈R…

Q: To what new value should f(1) be changed to remove the discontinuity? x2-4 x1 A.) -4 B.)-3 C.)-5…

A: Left sided limit at x=1 is:limx→1-f(x)=limx→1-(x2-4)=12-4=1-4=-3Right sided limit at x=1…

Q: 3 y" + 5y" + 6y" + 5y' + 3y = 0 %3D

A:

Q: 3. What is the domain of y =f°(e) # f(;)={-1°?

A:

Q: 5. Find the domain of the function: y = In () x-4

A: y=lnx-1x-4