3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200 x²

Q: Find the slope of the tangent line to the graphof the polar equation 1 TU r = at Ø 1-sino 6

A:

Q: A bank has decided to set its interest rates to compound monthly on all deposits in order to give…

A: We know the compound interest formula:A=P1+rnntwhere A=Principal amount +interest Amount…

Q: Find (a) v xw, (b) wxv, (c) vxv, and (d) wxw. v = i + 3j, w = 2i + 2j + 3k (a) v xw= (Type your…

A: Given query is to find indicated vector operation.

Q: The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the…

A: Given, f(x)=x24(1-x)

Q: aces)

A: We will find the value of the integral

Q: Find az/ax if z is a two variables function in x and y is defined implicitly by x5 + y² cos(x²₂³) =…

A: Here we have given a function : ⇒x5+y2cosx2z3=7xz+exz2 So for calculating ∂z∂x, y will be treated as…

Q: Find vertical asymptote, x intercept and y intercept of (x+1)(x-5)/(x-6)

A: Topic = Functions

Q: Using trigonometric substitution, A) None Ⓡ/ B Ⓒ D sec58d0 tan²0 tan40d0 sece * sinᎾdᎾ cosA Ss x4dx…

A: ∫x4(1+x2)32dxPerform trignometric substitutionSubstitute x=tan(θ)→θ=arctan(x)→dx=sec2θ dθ

Q: x6 cos(x³) A) True B) False |dx=0

A: We have to check by even or odd function

Q: For the function y =f(x), it was found out that f(c) = 0. What can be said that x=c? O critical…

A:

Q: ND THE AREA BOUNDED BY THE = x(x-1)², y-AXIS, AND THE =12

A:

Q: Find the transition points. y = 4x7 - 56x6 (Use symbolic notation and fractions where needed. Give…

A:

Q: * Ꮴ COS S 0 ( , ) Ꮎ d ᏧᎾ |2

A: To evaluate the given definite integral by using the Fundamental Theorem of Calculus, Part 2.∫0π…

Q: Using Simpson's method Blank 1 Add your answer √xdx for n=4 is equal to Blank 1 (use 2 decimal…

A:

Q: If you evaluate the integral expression 12x+1|dx the result is Blank 1 (use fraction or decimal in 2…

A: We have to integration

Q: Find the derivative of sin In x O sin(Inx)/x O cos(Inx)/x O cos(1/x) O sin (1/x)

A:

Q: 3.2x²+5dx A. In|2x² +51 + C A. B. C. * 4. 4. [ sec²x tanx dx A. tan²x + C 2 A. B. C. B. In|2x² +51…

A:

Q: 2 -dx for n=4 is equal to Blank 1 (use 2 decimal places with (x+2)² Using Trapezoidal method S…

A:

Q: ing Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: = Sx(t) - 2t²…

A:

Q: Given: parametric curve H defined by x(t) = tan¯¹t and y(t) = e¹t, where t € R (a) Find the slope of…

A: Given that parametric curve H defined by x(t) = tan-1t       and    y(t) = e4t , t ∈R           we…

Q: Find a particular solution of ds 1 π = cost determined by s=3 when t == = cos dt 3 ✓

A: Please see see below picture for detailed solution.

Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. (a) lim sin (2x6) sin(4x…

A: Explanation of the answer is as follows

Q: -4x⁹. sin(x) (1+x²)² dx=0

A: Follow the procedure given below.

Q: Iff is continuous on [a,b], then rtf(x) dx = π f(x) dx 1 A True B) False

A:

Q: What integration technique can be used to integrate: Integration Formulas O Trigonometric…

A:

Q: Use parametric equations to describe the solution set of the line equation below. Give the exact…

A:

Q: 5. Given that W 8.25 √y The value of x,y and z are measured with maximum percentage error of 1%, 2%…

A: Let's find maximum percentage error in w.

Q: Create a bucket by rotating around the y axis the curve y = 2 ln(x - 2) from y = 0 to y = 4. If this…

A:

Q: 5. f sin x cos x dx

A:

Q: x6 cos(x³) (A) True (B) False |dx=0

A: We will solve the problem

Q: Solve the differential equation: (x+y+2)dx-(x-y-4)dy=0

A: Solution

Q: Which of the following is not true? (A) None of the given choices 3 dx dx Ⓒ = S B S³ = In(x²) lim c→…

A: All Option are  correct So we have to choose Option 'A'

Q: C. Find the volume of the solid obtained by rotating the region bounded by y = -10 + 6x-x², x = 1…

A:

Q: -dx = 4 -2 X (A) True B) False m100

A:

Q: 4. Find the equation of the tangent lines to the curve y = √x and perpendicular to the line 14x +…

A: We have to find the tangent

Q: Which of the following is not true? A None of the given choices .3 dx dx S₁ in (x²) B lim S c+1+³c…

A: Let's solve.

Q: cos(x3 (A) True B) False dx=0

A: Here, x6cosx3 is an even function. So, ∫-11 x6cosx3dx≠0.

Q: 92%/ the first three terms in the malam Series of the funtion. f(x) = cos 22

A: We have to find the first three terms of the series.

Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: olve for the general solution using the Power Series. The answer was ready given, you just have to…

A: Please see the below picture for detailed solution.

Q: (1+x3)dy−x2ydx=0; y(1)=2

A:

Q: X X-2 such that (fog)(x) = x + 2. Q₁/ let f(x) = , find a function y = g(x)

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 2 ist dx for n=4 is equal to Blank 1 (use 2 decimal places with proper rounding off, no Jo (x + 2)²…

A: Given,  ∫012x+22dx ,  n=4

Q: Find the volume of R using shell method, when R is bounded by y = 4x - x², y = 0 about the line x =…

A:

Q: If you evaluate the integral expression 12x+1|dx the result is Blank 1 (use fraction or decimal in 2…

A:

Q: Given the function y=f(x), y" is found to be positive over the interval (4,8), then over this…

A: This question can be solved using the relation between second derivative and concavity of the…

Q: Find the transition points. f(x) = = x(5 - x)¹/3 (Use symbolic notation and fractions where needed.…

A:

Q: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: Given the function y=f(x), y' is found to be positive over the interval (4,8), then over this…

A: if the first derivative of function is positive, then the function is increasing.

Q: Given than han [ 1 (2) de = (z) dz=-4 and ® [1(e) de - [5 (2) de = 20 None of the given choices…

A: