To calculate: The equations of tangent to the given curve.
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Answer to Problem 46E
The equation of tangent line is y=−1−x−π .
Explanation of Solution
Given information:
The equation of the curve is y=sinx+cosx , x=π
Concept used:
The formulae used are ddx(sinx)=cosx , ddx(cosx)=−sinx .
Calculation:
Slope of tangent line.
m=dydx=ddx(sinx+cosx)=ddx(sinx)+ddx(cosx)=cosx−sinx
Solve further by substituting π for x in m=cosx−sinx
m=cosπ−sinπ=−1−0=−1
The slope of tangent line is −1
Substitute π for x in y=sinx+cosx for the value of y1 .
y=sinx+cosx=0+(−1)=−1
So, the value of (x1,y1)=(π,−1)
Substitute the values in the standard equation of line y−y1=m(x−x1)
y−(−1)=−1(x−π)y=−1−x−π
The equation of tangent line is y=−1−x−π.
Conclusion: The equation of tangent line is y=3−(x−π) , option (d) is correct.
Chapter 2 Solutions
CALCULUS-W/XL ACCESS
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