Let f(x) = 2(x − 1)^2 (2x + 1) be a function. Find all critical numbers of the function and determine whether a relative maximum, relative minimum, or neither occurs at each critical point.

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A: First draw the graph Uasing limits and the check the countinity of this function

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A: Solution is given below:

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A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: D. 32 В. -32 4. What is f y'(t)dt? A. - 16t2 - 100 t + C 16t2 - 100 t C. – 16t2 + 100 t + C D. -…

A: According to company rule, we can answer only First question and rest can be reposted.

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A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

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Q: 465.98 23.98 2.789 56.09 ATATA TTA TA

A: Rounding up

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A: As per our guidelines, we are supposed to answer only one question. Kindly repost other questions as…

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Q: Find div F and curl F if F (x, y, z) = 10e*V i – cos yj+ 3 sin zk. %3D div F= curl F=

A: div F=∂Fx∂x+∂Fy∂y+∂Fz∂z∂Fx∂x =ddx(10exy)=10y exy∂Fy∂y =ddy(-cos y)=sin y∂Fz∂z=ddz(3 sin2z)=3(2sinz…

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A: ∬Rx-16dA where R is the region in the first quadrant enclosed between y=x and y=x3

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A: Given, y= sqrt(25-x²) y= 4

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* 3 r(t) = e*i+e*j K(t)

A: First diffrenciate. And then put all the values in formula.

Q: 28) In Problems 28 and 29, given the IMPORTANT FORMULA x(a+1)+ C (if a2 -1) and x1 dx = In x + C.…

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Q: Use the formula «(t) = F () ×F (51 to find k(t). ||r(t)||* r(t) = t²i+t°j K(t) = %3D

A: We have t find κ(t) for the given vector r(t) = t2i + t5j The given formula is κ(t) =…

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Q: Find div F and curl F if F(x, y, z) = x°i – 10j + yzk. div F= curl F=

A: To find the divergence and curl of the following vectorF→=x9i-10j+yzk

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Q: Line segment AB is a diameter of the x² +y² + z² - 2z + 8y = 9. Find point B if A = (0, у, 0).

A: To find the point B if Coordinates  of A are given for the sphere.

Q: I. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) f'(x) lim = lim Equation 1…

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Q: Consider xy2+x2y=6, find the slope of the tangent line at the point (1, 2)

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Q: Find the area, A, of the region enclosed by the cardioid r = 8+8 cos 0.

A: Given   area can be given as below :

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Q: Find the indefinite integral. (Use c for the constant of integrat (4t3i + 4tj – 6vik) dt

A: we use the basic formula ∫xn dx =xn+1n+1+C    ; n≠-1

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Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

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Q: 4. Using logarithmic differentiation, or otherwise, find the derivative of y = (sin r)".

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Q: 2. lim

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